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New Developments of Dynamical Systems Theory for Diverse Mathematical Models

Research Project

Project/Area Number 17H02859
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field Foundations of mathematics/Applied mathematics
Research InstitutionKyoto University

Principal Investigator

Yagasaki Kazuyuki  京都大学, 情報学研究科, 教授 (40200472)

Co-Investigator(Kenkyū-buntansha) 伊藤 秀一  神奈川大学, 工学部, 教授 (90159905)
名和 範人  明治大学, 理工学部, 専任教授 (90218066)
Project Period (FY) 2017-04-01 – 2022-03-31
Project Status Completed (Fiscal Year 2022)
Budget Amount *help
¥17,550,000 (Direct Cost: ¥13,500,000、Indirect Cost: ¥4,050,000)
Fiscal Year 2021: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2020: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Fiscal Year 2019: ¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2018: ¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2017: ¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000)
Keywords力学系 / 可積分性 / 分岐 / 偏微分方程式 / ソリトン / ハミルトン系 / 結合振動子系 / 時間遅れ系 / 逆散乱法 / 最適制御 / 保存系 / 反転対称系 / 偏微分方程式系 / 第一積分 / 可換ベクトル場 / ネットワーク / 中心多様体 / 反転可能系 / ホモクリニック軌道 / パルス解 / 標準形 / 非可積分性 / 確率的な摂動を受ける系 / ソリトン解 / 力学系理論
Outline of Final Research Achievements

This project aims to develop new theories based on dynamical systems theory for diverse mathematical models that emerge in applied fields. In particular, we obtained significant results on the determination of real-analytic or complex-meromorphic nonintegrability for perturbations of integrable systems, on the analytic nonintegrability of dynamical systems having Poincare-Dulac normal forms of resonance degree two, on the integrability in the sense of differential Galois theory for the Zakharov-Shabat systems appearing in the inverse scattering method, which is a powerful technique for solving integrable partial differential equations such as the KdV equation, on the nonintegrability of the normal forms of fold-Hopf and double-Hopf codimension-two bifurcations, and on bifurcations and stability of the solitary wave solutions in partial differential equations.

Academic Significance and Societal Importance of the Research Achievements

円周制限3体問題は,3個の天体のうち1つの質量が零で残りの2個の天体が円運動するという3体問題の特殊なものであり,現代でも地球から月へのロケットの軌道設計を行う際に重要な数学モデルとなっている.3個の天体が平面上を運動する場合は1個,そうでない場合は2個の保存量があれば,2体問題の場合のようにこの問題が解けるが,100年以上前にポアンカレが2個の天体の質量比に依存した,必要な個数の保存量がないことを証明している.その後100年以上に渡って進展は見られなかったが,本研究で開発された複素有理型関数的な非可積分性の判定法を用いることにより,任意の質量比に対して制限3体問題の非可積分性が証明された.

Report

(6 results)
  • 2022 Final Research Report ( PDF )
  • 2021 Annual Research Report
  • 2020 Annual Research Report
  • 2019 Annual Research Report
  • 2018 Annual Research Report
  • 2017 Annual Research Report
  • Research Products

    (149 results)

All 2023 2022 2021 2020 2019 2018 2017 Other

All Int'l Joint Research (6 results) Journal Article (36 results) (of which Int'l Joint Research: 11 results,  Peer Reviewed: 34 results,  Open Access: 4 results) Presentation (107 results) (of which Int'l Joint Research: 24 results,  Invited: 16 results)

  • [Int'l Joint Research] University of Victoria(カナダ)

    • Related Report
      2021 Annual Research Report
  • [Int'l Joint Research] University of Victoria(カナダ)

    • Related Report
      2020 Annual Research Report
  • [Int'l Joint Research] Simon Bolivar大学(コロンビア)

    • Related Report
      2018 Annual Research Report
  • [Int'l Joint Research] Salome Urena教員養成高等機関(ドミニカ共和国)

    • Related Report
      2018 Annual Research Report
  • [Int'l Joint Research] Madrid工科大学(スペイン)

    • Related Report
      2018 Annual Research Report
  • [Int'l Joint Research] Simon Bolivar 大学(コロンビア)

    • Related Report
      2017 Annual Research Report
  • [Journal Article] Integrability of the Zakharov-Shabat systems by quadrature2023

    • Author(s)
      Yagasaki Kazuyuki
    • Journal Title

      Communications in Mathematical Physics

      Volume: - Issue: 1 Pages: 315-340

    • DOI

      10.1007/s00220-022-04610-8

    • Related Report
      2021 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Obstructions to integrability of nearly integrable dynamical systems near regular level sets2023

    • Author(s)
      Motonaga Shoya, Yagasaki Kazuyuki
    • Journal Title

      Archive for Rational Mechanics and Analysis

      Volume: -

    • Related Report
      2021 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Nonintegrability of nearly integrable dynamical systems near resonant periodic orbits2022

    • Author(s)
      Yagasaki Kazuyuki
    • Journal Title

      Journal of Nonlinear Science

      Volume: 32 Issue: 4

    • DOI

      10.1007/s00332-022-09802-z

    • Related Report
      2021 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Nonintegrability of dynamical systems near degenerate equilibria2022

    • Author(s)
      Yagasaki Kazuyuki
    • Journal Title

      Communications in Mathematical Physics

      Volume: 398 Issue: 3 Pages: 1129-1152

    • DOI

      10.1007/s00220-022-04545-0

    • Related Report
      2021 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Non-existence of ground states and gap of variational values for 3D Sobolev critical nonlinear scalar field equations2022

    • Author(s)
      Akahori Takafumi、Ibrahim Slim、Kikuchi Hiroaki、Nawa Hayato
    • Journal Title

      Journal of Differential Equations

      Volume: 334 Pages: 25-86

    • DOI

      10.1016/j.jde.2022.06.016

    • Related Report
      2021 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Optimal control of the SIR epidemic model based on dynamical systems theory2022

    • Author(s)
      Yagasaki Kazuyuki
    • Journal Title

      Discrete & Continuous Dynamical Systems - B

      Volume: 27 Issue: 5 Pages: 2501-2501

    • DOI

      10.3934/dcdsb.2021144

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Existence of finite time blow-up solutions in a normal form of the subcritical Hopf bifurcation with time-delayed feedback for small initial functions2022

    • Author(s)
      Yagasaki Kazuyuki
    • Journal Title

      Discrete & Continuous Dynamical Systems - B

      Volume: 27 Issue: 5 Pages: 2621-2621

    • DOI

      10.3934/dcdsb.2021151

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Analytic and algebraic conditions for bifurcations of homoclinic orbits II: Reversible systems2021

    • Author(s)
      Yagasaki Kazuyuki
    • Journal Title

      Journal of Dynamics and Differential Equations

      Volume: - Issue: 2 Pages: 1863-1884

    • DOI

      10.1007/s10884-021-10091-5

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Persistence of periodic and homoclinic orbits, first integrals and commutative vector fields in dynamical systems2021

    • Author(s)
      Motonaga Shoya、Yagasaki Kazuyuki
    • Journal Title

      Nonlinearity

      Volume: 34 Issue: 11 Pages: 7574-7608

    • DOI

      10.1088/1361-6544/ac24e4

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Numerical computations for bifurcations and spectral stability of solitary waves in coupled nonlinear Schr?dinger equations2021

    • Author(s)
      Yagasaki Kazuyuki、Yamazoe Shotaro
    • Journal Title

      Japan Journal of Industrial and Applied Mathematics

      Volume: 39 Issue: 1 Pages: 257-281

    • DOI

      10.1007/s13160-021-00485-9

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Global dynamics above the ground state energy for the combined power-type nonlinear Schrodinger equations with energy-critical growth at low frequencies2021

    • Author(s)
      Akahori Takafumi、Ibrahim Slim、Kikuchi Hiroaki、Hayato Nawa
    • Journal Title

      Memoirs of the American Mathematical Society

      Volume: 272 Issue: 1331

    • DOI

      10.1090/memo/1331

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Chebyshev spectral methods for computing center manifolds2021

    • Author(s)
      Saito Takeshi、Yagasaki Kazuyuki
    • Journal Title

      Journal of Computational Dynamics

      Volume: 8 Issue: 2 Pages: 165-165

    • DOI

      10.3934/jcd.2021008

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The Variational Structure of Potential Systems and Stability of Periodic Solutions2020

    • Author(s)
      柴山 允瑠
    • Journal Title

      Bulletin of the Japan Society for Industrial and Applied Mathematics

      Volume: 30 Issue: 1 Pages: 4-13

    • DOI

      10.11540/bjsiam.30.1_4

    • NAID

      130007867072

    • ISSN
      2432-1982
    • Year and Date
      2020-03-25
    • Related Report
      2019 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Bifurcations of radially symmetric solutions in a coupled elliptic system with critical growth in Rd for d?=?3,42020

    • Author(s)
      Yagasaki Kazuyuki、Stachowiak Tomasz
    • Journal Title

      Journal of Mathematical Analysis and Applications

      Volume: 484 Issue: 2 Pages: 123726-123726

    • DOI

      10.1016/j.jmaa.2019.123726

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Nonintegrability of the unfoldings of codimension-two bifurcations2020

    • Author(s)
      Acosta-Humanez Primitivo B、Yagasaki Kazuyuki
    • Journal Title

      Nonlinearity

      Volume: 33 Issue: 4 Pages: 1366-1387

    • DOI

      10.1088/1361-6544/ab60d4

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Numerical analyses for spectral stability of solitary waves near bifurcation points2020

    • Author(s)
      Yagasaki Kazuyuki、Yamazoe Shotaro
    • Journal Title

      Japan Journal of Industrial and Applied Mathematics

      Volume: 38 Issue: 1 Pages: 125-140

    • DOI

      10.1007/s13160-020-00428-w

    • NAID

      210000170327

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Bifurcations of homoclinic orbits in reversible systems2020

    • Author(s)
      Kazuyuki Yagasaki
    • Journal Title

      数理解析研究所講究録

      Volume: 2149

    • NAID

      120006888388

    • Related Report
      2019 Annual Research Report
  • [Journal Article] Fractal mechanism of basin of attraction in passive dynamic walking2020

    • Author(s)
      Okamoto Kota、Aoi Shinya、Obayashi Ippei、Kokubu Hiroshi、Senda Kei、Tsuchiya Kazuo
    • Journal Title

      Bioinspiration & Biomimetics

      Volume: 15 Issue: 5 Pages: 055002-055002

    • DOI

      10.1088/1748-3190/ab9283

    • NAID

      120006888011

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Heteroclinic Orbits and Nonintegrability in Two-Degree-of-Freedom Hamiltonian Systems with Saddle-Centers2019

    • Author(s)
      Yagasaki Kazuyuki、Yamanaka Shogo
    • Journal Title

      Symmetry, Integrability and Geometry: Methods and Applications

      Volume: 15

    • DOI

      10.3842/sigma.2019.049

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Nonintegrability and Chaos in Hamiltonian Systems with Saddle-Center2019

    • Author(s)
      Kazuyuki Yagasaki
    • Journal Title

      数理解析研究所講究録

      Volume: 2137

    • NAID

      120006888161

    • Related Report
      2019 Annual Research Report
  • [Journal Article] Uniqueness and nondegeneracy of ground states to nonlinear scalar field equations involving the Sobolev critical exponent in their nonlinearities for high frequencies2019

    • Author(s)
      Akahori T., Ibrahim S., Ikoma N., Kikuchi H. and Nawa H.
    • Journal Title

      Calculus of Variations and Partial Differential Equations

      Volume: 58 Issue: 4 Pages: 1-32

    • DOI

      10.1007/s00526-019-1556-6

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Explicit transversality conditions and local bifurcation diagrams for Bogdanov-Takens bifurcation on center manifolds2019

    • Author(s)
      Yang Li, Hiroshi Kokubu, and Kazuyuki Aihara
    • Journal Title

      Physica D

      Volume: 391 Pages: 52-65

    • DOI

      10.1016/j.physd.2018.11.005

    • Related Report
      2019 Annual Research Report 2018 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] The onset of transient turbulence in minimal plane Couette ow2019

    • Author(s)
      Julius Rhoan Lustro, Genta Kawahara, Lennaert van Veen, Masaki Shimizu, Hiroshi Kokubu
    • Journal Title

      Journal of Fluid Mechanics

      Volume: 862 Pages: 1-15

    • DOI

      10.1017/jfm.2018.971

    • Related Report
      2019 Annual Research Report 2018 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Topological computation analysis of meteorological time-series data.2019

    • Author(s)
      Morita, H., M. Inatsu, and H. Kokubu
    • Journal Title

      Journal of Society for Industrial and Applied Mathematics

      Volume: 18 Issue: 2 Pages: 1200-1212

    • DOI

      10.1137/18m1184746

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Variational proof of the existence of brake orbits in the planar 2-center problem2019

    • Author(s)
      Kajihara Yuika、,Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Yoshida-Honmachi, Sakyo-ku Kyoto 606-8501, Japan、Shibayama Misturu
    • Journal Title

      Discrete & Continuous Dynamical Systems - A

      Volume: 39 Issue: 10 Pages: 5785-5797

    • DOI

      10.3934/dcds.2019254

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Bifurcation of relative equilibria in infinite-dimensional Hamiltonian systems2019

    • Author(s)
      Kazuyuki Yagasaki, Shotaro Yamazoe
    • Journal Title

      SIAM Journal on Applied Dynamical Systems

      Volume: 18 Issue: 1 Pages: 393-417

    • DOI

      10.1137/18m1187738

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Global dynamics above the ground state energy for the combined power type nonlinear Schrodinger equations with energy critical growth at low frequencies2019

    • Author(s)
      Takafumi Akahori, Slim Ibrahim, Hiroaki Kikuchi, Hayato Nawa
    • Journal Title

      The Memoirs of the AMS

      Volume: 印刷中

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Uniqueness and nondegeneracy of ground states to nonlinear scalar field equations involving the Sobolev critical exponent in their nonlinearities for high frequencies2019

    • Author(s)
      Takafumi Akahori, Slim Ibrahim, Norihisa Ikoma, Hiroaki Kikuchi, Hayato Nawa
    • Journal Title

      Calculus of Variations and Partial Differential Equations

      Volume: 印刷中

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Variational Construction of Orbits Realizing Symbolic Sequences in the Planar Sitnikov Problem2019

    • Author(s)
      Shibayama Mitsuru
    • Journal Title

      Regular and Chaotic Dynamics

      Volume: 24 Issue: 2 Pages: 202-211

    • DOI

      10.1134/s1560354719020060

    • NAID

      120007173782

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Melnikov processes and chaos in randomly perturbed dynamical systems2018

    • Author(s)
      Kazuyuki Yagasaki
    • Journal Title

      Nonlinearity

      Volume: 31 Issue: 7 Pages: 3057-3085

    • DOI

      10.1088/1361-6544/aab89f

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Heteroclinic transition motions in periodic perturbations of conservative systems with an application to forced rigid body dynamics2018

    • Author(s)
      Kazuyuki Yagasaki
    • Journal Title

      Regular and Chaotic Dynamics

      Volume: 23 Issue: 4 Pages: 438-457

    • DOI

      10.1134/s1560354718040056

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Nonintegrability of parametrically forced nonlinear oscillators2018

    • Author(s)
      Shoya Motonaga, Kazuyuki Yagasaki
    • Journal Title

      Regular and Chaotic Dynamics

      Volume: 23 Issue: 3 Pages: 291-303

    • DOI

      10.1134/s156035471803005x

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Non-integrability of the spacial n-center problem2018

    • Author(s)
      Mitsuru Shibayama
    • Journal Title

      Journal of Differential Equations

      Volume: 印刷中 Issue: 6 Pages: 2461-2469

    • DOI

      10.1016/j.jde.2018.04.037

    • NAID

      120006601517

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Linear stability of periodic three-body orbits with zero angular momentum and topological dependence of Kepler’s third law: a numerical test2018

    • Author(s)
      Dmitrasinovic V、Hudomal Ana、Shibayama Mitsuru、Sugita Ayumu
    • Journal Title

      Journal of Physics A: Mathematical and Theoretical

      Volume: 51 Issue: 31 Pages: 315101-315101

    • DOI

      10.1088/1751-8121/aaca41

    • NAID

      120006601519

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Nonintegrability of the unfolding of the fold-Hopf bifurcation2018

    • Author(s)
      Kazuyuki Yagasaki
    • Journal Title

      Nonlinearity

      Volume: 31 Issue: 2 Pages: 341-350

    • DOI

      10.1088/1361-6544/aa92e8

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Periodic solutions of a perscribed-energy problem for a singular Hamiltonian system2017

    • Author(s)
      M. Shibayama
    • Journal Title

      Discrete and Continuous Dynamical Systems A

      Volume: 37 Issue: 5 Pages: 2705-2715

    • DOI

      10.3934/dcds.2017116

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed
  • [Presentation] 力学系に関連した 3 つの話題における最近の研究結果: KdV 方程式の特異ソリトン, Poincare-Dulac標準形の非可積分性, 余次元 2 の分岐の周期的摂動2023

    • Author(s)
      矢ヶ崎一幸
    • Organizer
      2022年度 冬の力学系研究集会
    • Related Report
      2021 Annual Research Report
  • [Presentation] シンプレクティック写像族のバーコフ標準化とハミルトン系の超可積分性2023

    • Author(s)
      伊藤秀一
    • Organizer
      日本数学会2022年度年会
    • Related Report
      2021 Annual Research Report
  • [Presentation] 力学系理論の手法による感染症数理モデル SEIR 系の最適制御2023

    • Author(s)
      竹口佳輝,矢ヶ崎一幸
    • Organizer
      日本数学会2023年度年会
    • Related Report
      2020 Annual Research Report
  • [Presentation] 力学系の非可積分性に関する最近の研究結果について2022

    • Author(s)
      矢ヶ崎一幸
    • Organizer
      2021年度 冬の力学系研究集会
    • Related Report
      2021 Annual Research Report
  • [Presentation] Some recent results on nonintegrability of dynamical systems2022

    • Author(s)
      矢ヶ崎一幸
    • Organizer
      RIMS共同研究(公開型)「幾何構造と微分方程式 ー対称性・特異点及び量子化の視点からー」
    • Related Report
      2021 Annual Research Report
  • [Presentation] 力学系の非可積分性に関する3つの話題2022

    • Author(s)
      矢ヶ崎一幸
    • Organizer
      RIMS共同研究(公開型)「力学系の理論と諸分野への応用」
    • Related Report
      2021 Annual Research Report
    • Invited
  • [Presentation] Three Topics on Nonintegrability of Dynamical Systems2022

    • Author(s)
      矢ヶ崎一幸
    • Organizer
      Integrability of the two-dimensional Zakharov-Shabat systems by quadrature
    • Related Report
      2021 Annual Research Report
  • [Presentation] Integrability of the two-dimensional Zakharov-Shabat systems by quadrature2022

    • Author(s)
      矢ヶ崎一幸
    • Organizer
      日本数学会2022年度秋季総合分科会
    • Related Report
      2021 Annual Research Report
  • [Presentation] Some recent results on nonintegrability of dynamical systems2022

    • Author(s)
      矢ヶ崎一幸
    • Organizer
      日本数学会2022年度秋季総合分科会
    • Related Report
      2021 Annual Research Report
  • [Presentation] Nonintegrability of three- and four-dimensional dynamical systems near degenerate equilibria2022

    • Author(s)
      矢ヶ崎一幸
    • Organizer
      日本数学会2022年度秋季総合分科会
    • Related Report
      2021 Annual Research Report
  • [Presentation] Birkhoff normalization for a family of superintegrable symplectic maps and its application2022

    • Author(s)
      伊藤秀一
    • Organizer
      RIMS共同研究(公開型)「幾何構造と微分方程式 ー対称性・特異点及び量子化の視点からー」
    • Related Report
      2021 Annual Research Report
    • Invited
  • [Presentation] 力学系理論を用いた感染症数理モデルSEIR系の最適制御2022

    • Author(s)
      竹口佳輝
    • Organizer
      RIMS共同研究(公開型)「力学系の理論と諸分野への応用」
    • Related Report
      2020 Annual Research Report
  • [Presentation] 力学系理論を用いた感染症数理モデルSEIR系の最適制御2022

    • Author(s)
      竹口佳輝
    • Organizer
      日本応用数理学会2022年度年会
    • Related Report
      2020 Annual Research Report
  • [Presentation] 共鳴不動点近傍におけるシンプレクティック写像族の超可積分性とバーコフ標準化2022

    • Author(s)
      伊藤秀一
    • Organizer
      2021年度冬の力学系研究集会
    • Related Report
      2020 Annual Research Report
  • [Presentation] Integrability of the Zakharov-Shabat systems by quadrature: An application of differential Galois theory to integrable nonlinear PDEs2021

    • Author(s)
      Yagasaki Kazuyuki
    • Organizer
      RIMS共同研究「力学系理論の最近の進展とその応用」
    • Related Report
      2021 Annual Research Report
  • [Presentation] 力学系の可積分性に関する 最近の研究結果について2021

    • Author(s)
      矢ヶ崎一幸
    • Organizer
      日本応用数理学会2021年度年会
    • Related Report
      2021 Annual Research Report
  • [Presentation] Integrability of the Zakharov-Shabat systems by quadrature: An application of differential Galois theory to integrable nonlinear PDEs2021

    • Author(s)
      矢ヶ崎一幸
    • Organizer
      日本応用数理学会2021年度年会
    • Related Report
      2021 Annual Research Report
  • [Presentation] 近可積分系に対する可積分性の判定2021

    • Author(s)
      本永翔也
    • Organizer
      2020年度冬の力学系研究集会
    • Related Report
      2019 Annual Research Report
  • [Presentation] Learning dynamics of the logistic maps by Reservoir Computing2021

    • Author(s)
      Hiroshi Kokubu
    • Organizer
      International Conference: Differential Equations for Data Science 2021 (DEDS2021)
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research
  • [Presentation] 近可積分系における第一積分の存在のための必要条件2020

    • Author(s)
      本永翔也 ,矢ヶ崎一幸
    • Organizer
      日本応用数理学会 2020年年会
    • Related Report
      2019 Annual Research Report
  • [Presentation] 複数のスパースグラフに依存する結合振動子ネットワークの連続極限2020

    • Author(s)
      伊原亮輔,矢ヶ崎一幸
    • Organizer
      日本応用数理学会 2020年年会
    • Related Report
      2019 Annual Research Report
  • [Presentation] Continuum limits of coupled oscillator networks depending on multiple sparse graphs2020

    • Author(s)
      矢ヶ崎一幸
    • Organizer
      RIMS研究集会「数理科学の諸問題と力学系理論の新展開」
    • Related Report
      2019 Annual Research Report
  • [Presentation] Existence of unbounded solutions in a normal form of the subcritical Hopf bifurcation with time-delayedfeedback for small initial functions2020

    • Author(s)
      矢ヶ崎一幸
    • Organizer
      RIMS研究集会「数理科学の諸問題と力学系理論の新展開」
    • Related Report
      2019 Annual Research Report
  • [Presentation] Chebyshev spectral methods for computing center manifolds2020

    • Author(s)
      矢ヶ崎一幸
    • Organizer
      RIMS研究集会「数理科学の諸問題と力学系理論の新展開」
    • Related Report
      2019 Annual Research Report
  • [Presentation] Optimal control of the SIR epidemic model2020

    • Author(s)
      矢ヶ崎一幸
    • Organizer
      RIMS研究集会「数理科学の諸問題と力学系理論の新展開」
    • Related Report
      2019 Annual Research Report
  • [Presentation] 近可積分系における第一積分の存在のための必要条件2020

    • Author(s)
      本永翔也
    • Organizer
      RIMS研究集会「数理科学の諸問題と力学系理論の新展開」
    • Related Report
      2019 Annual Research Report
  • [Presentation] 変分法によるポテンシャル系の孤立不変集合のコホモロジーの評価2020

    • Author(s)
      柴山允瑠
    • Organizer
      2019年度冬の力学系研究集会
    • Related Report
      2019 Annual Research Report
  • [Presentation] Variational construction of orbits realizing symbolic sequences in the planar Sitnikov problem2020

    • Author(s)
      Mitsuru Shibayama
    • Organizer
      Variational analysis of critical problems on nonlinear partial differential equations
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] トーラス上の面積保存写像の母関数の多価性と周期点の個数評価2020

    • Author(s)
      柴山允瑠
    • Organizer
      日本応用数理学会 2020年年会
    • Related Report
      2019 Annual Research Report
  • [Presentation] トーラス上の面積保存写像の母関数の多価性と周期点の個数評価2020

    • Author(s)
      柴山允瑠
    • Organizer
      RIMS 研究集会「数理科学の諸問題と力学系理論の新展開」
    • Related Report
      2019 Annual Research Report
  • [Presentation] 変分法による孤立不変集合のコホモロジーの評価2020

    • Author(s)
      柴山允瑠
    • Organizer
      RIMS 研究集会「数理科学の諸問題と力学系理論の新展開」
    • Related Report
      2019 Annual Research Report
  • [Presentation] Bifurcations of homoclinic orbits in reversible systems2019

    • Author(s)
      Kazuyuki Yagasaki
    • Organizer
      Equadiff 2019
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Pitchfork bifurcations and linear stability of solitary waves in coupled nonlinear Schrodinger equations2019

    • Author(s)
      Shotaro Yamazoe
    • Organizer
      Equadiff 2019
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Nonpersistence of periodic orbits, homoclinic orbits, first integrals, and commutative vector fields in perturbed systems2019

    • Author(s)
      Shoya Motonaga
    • Organizer
      Equadiff 2019
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Bifurcations and stability for one-parameter families of symmetric periodic orbits in reversible systems2019

    • Author(s)
      Kazuyuki Yagasaki
    • Organizer
      天体力学N体力学研究会
    • Related Report
      2019 Annual Research Report
  • [Presentation] Bifurcations and stability for one-parameter families of symmetric periodic orbits in reversible systems2019

    • Author(s)
      矢ヶ崎一幸
    • Organizer
      日本応用数理学会 2019年年会
    • Related Report
      2019 Annual Research Report
  • [Presentation] Pitchfork bifurcations and linear stability of solitary waves in coupled nonlinear Schrdinger equations2019

    • Author(s)
      矢ヶ崎一幸,山添祥太郎
    • Organizer
      日本応用数理学会 2019年年会
    • Related Report
      2019 Annual Research Report
  • [Presentation] 摂動系における周期軌道 , ホモクリニック軌道 , 第一積分および可換なベ クトル場の非保存 パート 2 適用例2019

    • Author(s)
      本永翔也,矢ヶ崎一幸
    • Organizer
      日本応用数理学会 2019年年会
    • Related Report
      2019 Annual Research Report
  • [Presentation] Bifurcations of homoclinic orbits in reversible systems2019

    • Author(s)
      Kazuyuki Yagasaki
    • Organizer
      RIMS研究集会「常微分方程式における最近の動向とその発展」
    • Related Report
      2019 Annual Research Report
    • Invited
  • [Presentation] ホモクリニック軌道の存在とカオスおよび分岐:サドル・センターから双曲的サドル, 双曲的サドルからサドル・センター,ハミルトン系から反転可能系へ2019

    • Author(s)
      矢ヶ崎一幸
    • Organizer
      第7回「ハミルトン系とその周辺」研究集会
    • Related Report
      2019 Annual Research Report
  • [Presentation] 可積分系の剛性とバーコフ標準形をめぐって2019

    • Author(s)
      伊藤秀一
    • Organizer
      第7回「ハミルトン系とその周辺」研究集会
    • Related Report
      2019 Annual Research Report
    • Invited
  • [Presentation] Morse decomposition of dynamics from time-series data2019

    • Author(s)
      國府寛司
    • Organizer
      Workshop on Data Analysis and Machine Learning in Dynamical Systems
    • Related Report
      2019 Annual Research Report
    • Invited
  • [Presentation] Morse decomposition of dynamics from time-series data and its application2019

    • Author(s)
      Hiroshi Kokubu
    • Organizer
      EASIAM
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Variational approach to the theory of isolated invariant sets for potential systems2019

    • Author(s)
      柴山允瑠
    • Organizer
      天体力学N体力学研究会
    • Related Report
      2019 Annual Research Report
  • [Presentation] ポテンシャル系の孤立不変集合のコホモロジーの評価2019

    • Author(s)
      柴山允瑠
    • Organizer
      日本応用数理学会 2019年年会
    • Related Report
      2019 Annual Research Report
  • [Presentation] 変分法によるポテンシャル系の孤立不変集合のコホモロジーの評価2019

    • Author(s)
      柴山允瑠
    • Organizer
      第9回岐阜数理科学研究会
    • Related Report
      2019 Annual Research Report
  • [Presentation] 平面 Sitnikov 問題における記号列を実現する軌道と周期軌道の存在2019

    • Author(s)
      柴山允瑠
    • Organizer
      2019年度日本数学会秋季総合分科会
    • Related Report
      2019 Annual Research Report
  • [Presentation] 変分法によるポテンシャル系の孤立不変集合のコホモロジーの評価2019

    • Author(s)
      柴山允瑠
    • Organizer
      第7回「ハミルトン系とその周辺」研究集会
    • Related Report
      2019 Annual Research Report
  • [Presentation] Bifurcations of homoclinic orbits in reversible systems and an application to radially symmetric solutions in a coupled elliptic system2019

    • Author(s)
      矢ヶ崎一幸
    • Organizer
      冬の力学系研究集会
    • Related Report
      2018 Annual Research Report
  • [Presentation] 摂動系における周期軌道,ホモクリニック軌道,第一積分および可換なベクトル場の非保存2019

    • Author(s)
      本永翔也
    • Organizer
      冬の力学系研究集会
    • Related Report
      2018 Annual Research Report
  • [Presentation] Bifurcations of radially symmetric solutions in a coupled elliptic systemwith critical exponents2019

    • Author(s)
      矢ヶ崎一幸,Tomasz Stachowiak
    • Organizer
      日本数学会2019年度年会
    • Related Report
      2018 Annual Research Report
  • [Presentation] 摂動系における周期軌道,ホモクリニック軌道,第一積分および可換なベクトル場の非保存2019

    • Author(s)
      本永翔也,矢ヶ崎一幸
    • Organizer
      日本数学会2019年度年会
    • Related Report
      2018 Annual Research Report
  • [Presentation] Bifurcations of homoclinic orbits in reversible systems2019

    • Author(s)
      矢ヶ崎一幸
    • Organizer
      日本数学会2019年度年会
    • Related Report
      2018 Annual Research Report
  • [Presentation] Action-angle coordinates near singularities for noncommutatively integrable Hamiltonian systems2019

    • Author(s)
      Hidekazu Ito
    • Organizer
      Conference on PDEs, Dynamical Systems and Probability
    • Related Report
      2018 Annual Research Report
    • Invited
  • [Presentation] 非線形シュレーディンガー方程式の重対数法則とブラウン運動の重複対数の法則2019

    • Author(s)
      名和範人
    • Organizer
      関西確率論セミナー
    • Related Report
      2018 Annual Research Report
  • [Presentation] 一般的な相互作用力による平面三体問題の非可積分性について2019

    • Author(s)
      山田淳二,柴山允瑠
    • Organizer
      日本数学会2019年度年会
    • Related Report
      2018 Annual Research Report
  • [Presentation] 変分法による平面2中心問題におけるbrake軌道の存在証明2019

    • Author(s)
      梶原唯加,柴山允瑠
    • Organizer
      日本数学会2019年度年会
    • Related Report
      2018 Annual Research Report
  • [Presentation] 余次元2の標準形の非可積分性2018

    • Author(s)
      矢ヶ崎一幸
    • Organizer
      RIMS共同研究集会(公開型)力学系 ―理論と応用の融合―
    • Related Report
      2018 Annual Research Report
  • [Presentation] 複数のグラフに依存する結合振動子系の連続極限2018

    • Author(s)
      伊原亮輔
    • Organizer
      RIMS共同研究集会(公開型)力学系 ―理論と応用の融合―
    • Related Report
      2018 Annual Research Report
  • [Presentation] Nonintegrability of the unfoldings of codomension-two bifurcations2018

    • Author(s)
      Kazuyuki Yagasaki
    • Organizer
      International Conference on Algebraic Methods in Dynamical Systems
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Heteroclinic orbits and nonintegrability in two-degree-of-freedom Hamiltonian systems with saddle-centers2018

    • Author(s)
      Kazuyuki Yagasaki, Shogo Yamanaka
    • Organizer
      International Conference on Algebraic Methods in Dynamical Systems
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Nonintegrability of parametrically forced nonlinear oscillators2018

    • Author(s)
      Shoya Motonaga, Kazuyuki Yagasaki
    • Organizer
      International Conference on Algebraic Methods in Dynamical Systems
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Bifurcation of relative equilibria in infinite-dimensional Hamiltonian systems2018

    • Author(s)
      Shotaro Yamazoe
    • Organizer
      The 12th AIMS Conference on Dynamical Systems, Differential Equations and Applications
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research
  • [Presentation] 余次元2の分岐に対する標準形の非可積分性2018

    • Author(s)
      Primitivo B. Acosta-Humanez, 矢ヶ崎一幸
    • Organizer
      日本応用数理学会2018年度年会
    • Related Report
      2018 Annual Research Report
  • [Presentation] 2自由度ハミルトン系における横断的なヘテロクリニック軌道の存在と非可積分性2018

    • Author(s)
      矢ヶ崎一幸,山中祥五
    • Organizer
      日本応用数理学会2018年度年会
    • Related Report
      2018 Annual Research Report
  • [Presentation] 摂動系における周期軌道,ホモクリニック軌道,第一積分および可換なベクトル場の非保存2018

    • Author(s)
      本永翔也,矢ヶ崎一幸
    • Organizer
      日本応用数理学会2018年度年会
    • Related Report
      2018 Annual Research Report
  • [Presentation] 複数のグラフに依存する結合振動子系の連続極限2018

    • Author(s)
      伊原亮輔,矢ヶ崎一幸
    • Organizer
      日本応用数理学会2018年度年会
    • Related Report
      2018 Annual Research Report
  • [Presentation] Chaos in randamly perturbed dynamical systems2018

    • Author(s)
      矢ヶ崎一幸
    • Organizer
      日本数学会2018年度秋季総合分科会
    • Related Report
      2018 Annual Research Report
  • [Presentation] Nonintegrability of parametrically forced nonlinear oscillators2018

    • Author(s)
      本永翔也,矢ヶ崎一幸
    • Organizer
      日本数学会2018年度秋季総合分科会
    • Related Report
      2018 Annual Research Report
  • [Presentation] Nonintegrability and chaos in Hamiltonian systems with saddle-centers2018

    • Author(s)
      Kazuyuki Yagasaki
    • Organizer
      RIMS共同研究(公開型)幾何構造と微分方程式 ―対称性と特異点の視点から―
    • Related Report
      2018 Annual Research Report
  • [Presentation] Nonpersistence of periodic orbits, homoclinic orbits, first integrals, and commutative vector fields in perturbed systems2018

    • Author(s)
      Shoya Motonaga
    • Organizer
      RIMS共同研究(公開型)幾何構造と微分方程式 ―対称性と特異点の視点から―
    • Related Report
      2018 Annual Research Report
  • [Presentation] 複数のグラフに依存する結合振動子系の連続極限2018

    • Author(s)
      伊原亮輔,矢ヶ崎一幸
    • Organizer
      2018年度応用数学合同研究集会
    • Related Report
      2018 Annual Research Report
  • [Presentation] 摂動系における周期軌道,ホモクリニック軌道,第一積分および可換なベクトル場の非保存2018

    • Author(s)
      本永翔也,矢ヶ崎一幸
    • Organizer
      2018年度応用数学合同研究集会
    • Related Report
      2018 Annual Research Report
  • [Presentation] 非線形 Schrodinger方程式とNelson拡散過程2018

    • Author(s)
      名和範人
    • Organizer
      平成30年度確率論シンポジウム
    • Related Report
      2018 Annual Research Report
  • [Presentation] Computer-assisted approach to global dynamics of multi-parameter systems2018

    • Author(s)
      Hiroshi Kokubu
    • Organizer
      KSIAM Spring Conference
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] ダイナミクスの数学 ―失敗から生まれた研究分野とその発展―2018

    • Author(s)
      國府寛司
    • Organizer
      失敗学会夏の大会
    • Related Report
      2018 Annual Research Report
    • Invited
  • [Presentation] Morse decomposition of the switching system and its smooth perturbations2018

    • Author(s)
      Hiroshi Kokubu
    • Organizer
      International Conference on Algebraic Topology in Data and Dyamics (The 60th birthday conference in honor of Konstantin Mischaikow)
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] 平面Sitnikov問題における周期解とヘテロクリニック軌道について2018

    • Author(s)
      柴山允瑠
    • Organizer
      RIMS共同研究集会(公開型)力学系 ―理論と応用の融合―
    • Related Report
      2018 Annual Research Report
  • [Presentation] Variational construction of periodic and heteroclinic orbits in the planar Sitnikov problem2018

    • Author(s)
      Mitsuru Shibayama
    • Organizer
      HAMSYS 2018
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Variational proof of the existence of brake orbits in the planer 2-center problem2018

    • Author(s)
      Yuika Kajihara
    • Organizer
      HAMSYS 2018
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Variational construction of periodic and heteroclinic orbits in the planar Sitnikov problem2018

    • Author(s)
      Mitsuru Shibayama
    • Organizer
      The 12th AIMS Conference on Dynamical Systems
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Variational construction of periodic and heteroclinic orbits in the planar Sitnikov problem2018

    • Author(s)
      Mitsuru Shibayama
    • Organizer
      Boston University/Keio University Workshop 2018 - Dynamical Systems
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Non-integrability of the spatial n-center and restricted n+1-body problem2018

    • Author(s)
      Mitsuru Shibayama
    • Organizer
      Hamiltonian Systems, from Topology to Applications through Analysis II
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Variational proof of the existence of brake orbits in the planer 2-center problem2018

    • Author(s)
      Yuika Kajihara
    • Organizer
      Hamiltonian Systems, from Topology to Applications through Analysis II
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research
  • [Presentation] 連続極限によるネットワーク上の制御系設計について2018

    • Author(s)
      伊原亮輔
    • Organizer
      冬の力学系研究集会
    • Related Report
      2017 Annual Research Report
  • [Presentation] Nonintegrability of parametrically forced nonlinear oscillators2018

    • Author(s)
      本永翔也
    • Organizer
      冬の力学系研究集会
    • Related Report
      2017 Annual Research Report
  • [Presentation] Nonintegrability of the unfoldings of codomension-two bifurcations2018

    • Author(s)
      矢ヶ崎一幸
    • Organizer
      天体力学N体力学研究会
    • Related Report
      2017 Annual Research Report
  • [Presentation] Bifurcations of relative equilibria in infinite-dimensional Hamiltonian systems2018

    • Author(s)
      Kazuyuki Yagasaki, Shotaro Yamazoe
    • Organizer
      The Third International Conference on the Dynamics of Differential Equations
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research
  • [Presentation] 2自由度ハミルトン系における横断的なヘテロクリニック軌道の存在と非可積分性2018

    • Author(s)
      矢ヶ崎一幸,山中祥五
    • Organizer
      日本数学会2018年度年会
    • Related Report
      2017 Annual Research Report
  • [Presentation] Stability and bifurcations of some simple models of the human bipedal locomotion2018

    • Author(s)
      Hiroshi Kokubu
    • Organizer
      The Third International Conference on the Dynamics of Differential Equations
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] 平面Sitnikov問題における記号力学系と変分構造2018

    • Author(s)
      柴山允瑠
    • Organizer
      天体力学N体力学研究会
    • Related Report
      2017 Annual Research Report
  • [Presentation] シンプレクティック写像の不動点のモース指数と安定性2018

    • Author(s)
      柴山允瑠
    • Organizer
      天体力学N体力学研究会
    • Related Report
      2017 Annual Research Report
  • [Presentation] fold-Hopf 分岐に対する標準形の非可積分性2017

    • Author(s)
      矢ヶ崎一幸
    • Organizer
      RIMS共同研究 力学系ー理論と応用の連携探索
    • Related Report
      2017 Annual Research Report
  • [Presentation] Bifurcations of radially symmetric solutions in a coupled ell iptic system with critical exponents2017

    • Author(s)
      Tomasz Stachowiak, Kazuyuki Yagasaki
    • Organizer
      日本応用数理学会2017年度年会
    • Related Report
      2017 Annual Research Report
  • [Presentation] 非線形波動方程式のソリトン解に対する数値分岐解析2017

    • Author(s)
      矢ヶ崎一幸,山添祥太郎
    • Organizer
      日本応用数理学会2017年度年会
    • Related Report
      2017 Annual Research Report
  • [Presentation] Fold-Hopf分岐に対する標準形の非可積分性2017

    • Author(s)
      矢ヶ崎一幸
    • Organizer
      日本数学会2017年度秋季総合分科会
    • Related Report
      2017 Annual Research Report
  • [Presentation] ハミルトン系における横断的なヘテロクリニック軌道と非可積分性2017

    • Author(s)
      山中祥五,矢ヶ崎一幸
    • Organizer
      2017年度応用数学合同研究集会
    • Related Report
      2017 Annual Research Report
  • [Presentation] 無限次元Hamilton系における相対定常解の分岐と非線形Schrodinger方程式への応用2017

    • Author(s)
      矢ヶ崎一幸,山添祥太郎
    • Organizer
      2017年度応用数学合同研究集会
    • Related Report
      2017 Annual Research Report
  • [Presentation] ベクトル場と写像に対する可積分性と標準形理論2017

    • Author(s)
      伊藤秀一
    • Organizer
      「微分方程式と幾何学」研究集会
    • Related Report
      2017 Annual Research Report
  • [Presentation] Birkhoff normalization of non-commutatively integrable symplectic maps and its applications2017

    • Author(s)
      Hidekazu Ito
    • Organizer
      "Analysis and Dynamics" Conference in occasion of Luigi Chierchia's 60th birthday
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Stability of bipedal locomotion: a dynamical system approach2017

    • Author(s)
      Hiroshi Kokubu
    • Organizer
      2017 International Workshop on Industrial and Applied Mathematics
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Global dynamics of systems with steep nonlinearities2017

    • Author(s)
      Hiroshi Kokubu
    • Organizer
      Mathematical Congress of the Americas
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] A new hysteresis mechanism in hybrid dynamical systems - Toward understanding the walk-run transition in human bipedal locomotion -2017

    • Author(s)
      Hiroshi Kokubu
    • Organizer
      A3 joint Workshop on Fluid Dynamics and Material Science
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Non-integrability of the restricted n-body problem2017

    • Author(s)
      Mitsuru Shibayama
    • Organizer
      RIMS共同研究 界面運動,力学系に現れる漸近問題への粘性解的手法とその周辺
    • Related Report
      2017 Annual Research Report
    • Invited
  • [Presentation] 制限n体問題の非可積分性2017

    • Author(s)
      柴山允瑠
    • Organizer
      日本応用数理学会2017年度年会
    • Related Report
      2017 Annual Research Report
  • [Presentation] 制限n体問題の非可積分性2017

    • Author(s)
      柴山允瑠
    • Organizer
      日本数学会秋季総合分科会
    • Related Report
      2017 Annual Research Report
  • [Presentation] ケプラー型ポテンシャル系のエネルギー固定問題における周期解の存在2017

    • Author(s)
      柴山允瑠
    • Organizer
      日本数学会秋季総合分科会
    • Related Report
      2017 Annual Research Report

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Published: 2017-04-28   Modified: 2024-01-30  

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