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2008 Fiscal Year Final Research Report

Topological and computational methods for dynamical systems basedon the theory of Conley index

Research Project

  • PDF
Project/Area Number 17540206
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Global analysis
Research InstitutionRyukoku University

Principal Investigator

OKA Hiroe (國府 宏枝)  Ryukoku University, 理工学部, 教授 (20215221)

Co-Investigator(Renkei-kenkyūsha) ARAI Zin  北海道大学, 創成科学共同研究機構, 特任助教 (80362432)
ISHII Yutaka  九州大学, 大学院・数理学研究院, 准教授 (20304727)
KOKUBU Hiroshi  京都大学, 大学院・理学研究科, 教授 (50202057)
Project Period (FY) 2005 – 2008
Keywords力学系 / 分岐 / カオス / 計算的方法 / Conley指数
Research Abstract

位相的方法を精度保証付きの計算的方法と組み合わせて力学系の大域的構造と分岐について厳密な計算機支援解析の方法を開拓し以下のような問題を解決した.
・特異摂動的ベクトル場のConley指数理論の拡張
・非線形ダイナミクスの大域的構造や分岐を調べる位相的アルゴリズムの構築とLeslieモデルへの応用
・Logistic写像の臨界点近傍の外での一様双曲性に関するMane条件を満たすパラメータ集合を求める方法
・Henon写像の双曲性パラメータ集合を求める方法とその記号力学系的性質

  • Research Products

    (12 results)

All 2008 2007 2006 2005 Other

All Journal Article (9 results) (of which Peer Reviewed: 9 results) Presentation (3 results)

  • [Journal Article] Quantitative hyperbolicity estimates in one-dimensional dynamics2008

    • Author(s)
      S. Day, H. Kokubu, S. Luzzatto, K. Mischaikow, H. Oka, P. Pilarczyk
    • Journal Title

      Nonlinearity 21

      Pages: 1967-1987

    • Peer Reviewed
  • [Journal Article] On hyperbolic plateaus of the Henon map2007

    • Author(s)
      Z.Arai
    • Journal Title

      Experiment. Math. 16 no.2

      Pages: 181-188

    • Peer Reviewed
  • [Journal Article] Topological horseshoes of travelling waves for a fast-slow predator-prey system2007

    • Author(s)
      M. Gameiro, T. Gedeon, W. Kalies, H. Kokubu, K. Mischaikow, H. Oka
    • Journal Title

      J. Dyn. Diff. Eq. 19

      Pages: 623-654

    • Peer Reviewed
  • [Journal Article] Rigorous verification of the cocoon bifurcation in the Michelson system2007

    • Author(s)
      H. Kokubu, D. Wilczak, P. Zgliczynski
    • Journal Title

      Nonlinearity 20

      Pages: 2147-2174

    • Peer Reviewed
  • [Journal Article] Note on a paper by Kawasaki and Sasa on Bernoulli coupled map lattices2006

    • Author(s)
      Yutaka Ishii
    • Journal Title

      J. Phys. A39 no.45

      Pages: 14043-14046

    • Peer Reviewed
  • [Journal Article] Rigorous computationsof homoclinic tangencies2006

    • Author(s)
      Z. Arai, K. Mischaikow
    • Journal Title

      SIAM J. Appl. Dyn. Syst. 5

      Pages: 280-292

    • Peer Reviewed
  • [Journal Article] The Conley index for fast-slow systems II : Multi-dimensional slow variable2006

    • Author(s)
      T. Gedeon, H. Kokubu, K. Mischaikow, H. Oka
    • Journal Title

      J. Diff. Eq. 225

      Pages: 242-307

    • Peer Reviewed
  • [Journal Article] Conley index theory for slow-fastsystems : multi-dimensional slow manifold2005

    • Author(s)
      Hiroe Oka
    • Journal Title

      Proceedings of International Conference on Differential Equations, Hasselt

      Pages: 912-917

    • Peer Reviewed
  • [Journal Article] A Database Schema for the Analysis of Global Dynamics of Multiparameter Systems

    • Author(s)
      Z. Arai, H. Kokubu, S. Luzzatto, K. Mischaikow, H. Oka, P. Pilarczyk
    • Journal Title

      SIAM Journal on Applied Dynamical Systems (掲載確定)

    • Peer Reviewed
  • [Presentation] Bifurcation of Morsedecompositions : A case study International Conference on Foundation of Computational Mathematics2008

    • Author(s)
      H. Kokubu
    • Organizer
      City University of Hong Kong
    • Place of Presentation
      Hong Kong, P.R.China
    • Year and Date
      20080616-18
  • [Presentation] Some bifurcations in the database ofthe Leslie model2008

    • Author(s)
      H. Oka
    • Organizer
      Computational Topologyand Dynamics Workshop
    • Place of Presentation
      State University
    • Year and Date
      2008-08-12
  • [Presentation] Application of topological singularperturbation theory to travelling waves in apredator-prey system2005

    • Author(s)
      H. Oka
    • Organizer
      CIRM
    • Place of Presentation
      Luminy, France
    • Year and Date
      20050704-08

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Published: 2010-06-10   Modified: 2016-04-21  

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