Research on random real and complex dynamical systems, semigroups of holomorphic maps and fractal geometry

• Project/Area Number: 19H01790
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Single-year Grants
• Section: 一般
• Review Section: Basic Section 12010:Basic analysis-related
• Research Institution: Kyoto University
• Principal Investigator: 角 大輝 京都大学, 人間・環境学研究科, 教授 (40313324)
• Co-Investigator(Kenkyū-buntansha): 中西 敏浩 島根大学, 学術研究院理工学系, 教授 (00172354) ; 佐藤 譲 北海道大学, 電子科学研究所, 准教授 (30342794) ; 上原 崇人 岡山大学, 環境生命自然科学学域, 准教授 (40613261) ; 諸澤 俊介 高知大学, 教育研究部自然科学系理工学部門, 教授 (50220108) ; イェーリッシュ ヨハネス 名古屋大学, 多元数理科学研究科, 准教授 (90741869) ; 和田 昌昭 大阪大学, 大学院情報科学研究科, 名誉教授 (80192821)
• Project Period (FY): 2019-04-01 – 2024-03-31
• Project Status: Completed (Fiscal Year 2023)
• Budget Amount: ¥17,420,000 (Direct Cost: ¥13,400,000、Indirect Cost: ¥4,020,000); Fiscal Year 2023: ¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000); Fiscal Year 2022: ¥2,470,000 (Direct Cost: ¥1,900,000、Indirect Cost: ¥570,000); Fiscal Year 2021: ¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000); Fiscal Year 2020: ¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000); Fiscal Year 2019: ¥6,240,000 (Direct Cost: ¥4,800,000、Indirect Cost: ¥1,440,000)
• Keywords: ランダム複素力学系 / ランダム力学系 / 正則写像半群 / フラクタル / ランダム性誘起現象 / ジュリア集合 / ランダム緩和ニュートン法 / マルコフ的複素力学系 / 力学系

Outline of Research at the Start

(A) ランダムな実および複素力学系、(B) 写像の半群の力学系、多価写像の力学系、(C) フラクタル幾何学の研究を行う。「力学系理論」では、物事がある規則に従って時間とともに変化する様子を探るが、自然界や社会現象ではランダム項が存在するので、その規則がランダムに変化するようなランダム力学系の研究が必要となる。ランダム性がもたらす新しい現象の発見とそのメカニズムの解明を行う。それに関連して多価写像の力学系やフラクタルの研究を行うことが重要である。それらを全て合わせて総合的に多角的に研究を行っていく。

Outline of Annual Research Achievements

角は高次元ランダム複素力学系の研究を行い、一つの正則写像の反復合成による力学系では起こりえない多くの新しい現象を考察した。特に複素２次元の一般化エノン写像のランダム力学系の分岐、複素２次元ランダム緩和ニュートン法の収束性と安定性について結果を得た。その際に高次元特有の困難さを乗り越える方法を編み出した。また、高次元複素射影空間上の正則写像のランダム力学系について、弱い安定性についての結果をいくつか得ることができた。さらに、アメリカのM. Comerford氏との共同研究において、非有界多項式列のジュリア集合の非一様完全性などの、通常の一つの多項式の反復では起こりえない新しい現象を詳しく研究して複数の結果を得た。さらにイエーリッシュ氏、渡邉氏（中部大）と双曲的なマルコフ的複素力学系のジュリア集合の次元と測度についての結果を得た。これらの結果について複数の研究集会で発表し、いくつかの結果については研究論文の準備に取りかかった。
上原は有理曲面上の双有理写像に対して、その力学系の複雑さを表す力学系的次数全体のなす集合の構造について調べた。中西は写像類群のタイヒミュラー空間への作用の有理変換表現と曲面群の3次元双曲等長変換群への行列表現を用いて境界群と呼ばれるクライン群のいくつかの具体例を構成し、残留極限点をもつクライン群など特徴的性質をもつクライン群を見つけて考察した。
諸澤は有理関数の半群の力学系とinner composite functions の力学系の研究を行った。イエーリッシュは無限生成フックス群のポアンカレ指数についてグラフの従順性の観点から研究を行った。また佐藤はランダム力学系と確率微分方程式で生じる確率カオスと関連する確率的非線形現象に関する研究を行い、研究会Dynamics Daysを東京工業大学、東京理科大学にて開催した。

Research Progress Status

令和5年度が最終年度であるため、記入しない。

Strategy for Future Research Activity

令和5年度が最終年度であるため、記入しない。

Research Products

• [Int'l Joint Research] University of Rhode Island(米国)
• [Int'l Joint Research] Universidade Federal do Rio de Janeiro/Univ. Federal do Vale do Sao Francisco/UFRJ(ブラジル)
• [Int'l Joint Research] University of Reading/Queen Mary University of London(英国)
• [Int'l Joint Research] ICTP/SISSA(イタリア)
• [Int'l Joint Research] Max Planck Institute, Dresden(ドイツ)
• [Int'l Joint Research] University of Rhode Island(米国)
• [Int'l Joint Research] University of Bremen(ドイツ)
• [Int'l Joint Research] Ball State University/University of Rhode Island(米国)
• [Int'l Joint Research] Christian-Albrechts-Universitaet zu Kiel/University of Bremen/Max Planck Institute, Dresden(ドイツ)
• [Int'l Joint Research] University in Krakow(ポーランド)
• [Int'l Joint Research] UFRJ(ブラジル)
• [Int'l Joint Research] University of Reading(英国)
• [Int'l Joint Research]
• [Int'l Joint Research] Ball State University/University of Rhode Island(米国)
• [Int'l Joint Research] Christian-Albrechts-Universitaet zu Kiel/University of Bremen(ドイツ)
• [Int'l Joint Research] University in Krakow(ポーランド)
• [Int'l Joint Research] University of North Texas/Ball State University/University of Rhode Island(米国)
• [Int'l Joint Research] Christian-Albrechts-Universitaet zu Kiel/University of Bremen(ドイツ)
• [Int'l Joint Research] University in Krakow(ポーランド)
• [Int'l Joint Research] Queen Mary University of London(英国)
• [Int'l Joint Research] CNRS(フランス)
• [Int'l Joint Research]
• [Journal Article] Heterogeneity of the attractor of the Lorenz ’96 model: Lyapunov analysis, unstable periodic orbits, and shadowing properties (2024)
  • Author(s): Chiara Cecilia Maiocchi, Valerio Lucarini, Andrey Gritsun, and Yuzuru Sato
  • Journal Title: Physica D Volume: 457 Pages: 133970-133970
  • DOI: 10.1016/j.physd.2023.133970
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Transition to anomalous dynamics in a simple random map (2024)
  • Author(s): Jin Yan, Moitrish Majumdar, Stefano Ruffo, Yuzuru Sato, Christian Beck, and Rainer Klages.
  • Journal Title: Chaos Volume: 34 Issue: 2 Pages: 023128-023128
  • DOI: 10.1063/5.0176310
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Siegel Disks on Rational Surfaces (2023)
  • Author(s): T. Uehara
  • Journal Title: Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl. Volume: 34
  • Peer Reviewed / Open Access
• [Journal Article] A gluing construction of projective K3 surfaces (2022)
  • Author(s): T. Koike, T. Uehara
  • Journal Title: Epijournal de Geometrie Algebrique Volume: 6
  • Peer Reviewed / Open Access
• [Journal Article] Non-i.i.d. random holomorphic dynamical systems and the generic dichotomy (2022)
  • Author(s): Hiroki Sumi and Takayuki Watanabe
  • Journal Title: Nonlinearity Volume: 35 Issue: 4 Pages: 1857-1875
  • DOI: 10.1088/1361-6544/ac4a89
  • Peer Reviewed
• [Journal Article] Negativity of Lyapunov Exponents and Convergence of Generic Random Polynomial Dynamical Systems and Random Relaxed Newton’s Methods (2021)
  • Author(s): Hiroki Sumi
  • Journal Title: Communications in Mathematical Physics Volume: 384 Issue: 3 Pages: 1513-1583
  • DOI: 10.1007/s00220-021-04070-6
  • Peer Reviewed
• [Journal Article] Uniformly perfect and hereditarily non uniformly perfect analytic and conformal non-autonomous attractor sets (2021)
  • Author(s): Mark Comerford、Kurt Falk、Rich Stankewitz、Hiroki Sumi
  • Journal Title: Dynamical Systems Volume: 36 Issue: 4 Pages: 631-655
  • DOI: 10.1080/14689367.2021.1975262
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Teichmüller space and the mapping class group of the twice punctured torus (2021)
  • Author(s): Toshihiro NAKANISHI
  • Journal Title: Journal of the Mathematical Society of Japan Volume: 73 Issue: 4 Pages: 1221-1252
  • DOI: 10.2969/jmsj/84998499
  • NAID: 130008106922
  • ISSN: 0025-5645, 1881-1167, 1881-2333
  • Peer Reviewed
• [Journal Article] Projective Hausdorff measure for Cantor sets (2021)
  • Author(s): Masaaki Wada
  • Journal Title: 数理解析研究所講究録 Volume: 2176
  • NAID: 120007141900
• [Journal Article] Existence of exceptional points for Fuchsian groups of finite coarea (2020)
  • Author(s): Toshihiro Nakanishi and Akira Ushijima
  • Journal Title: Conformal Geometry and Dynamics Volume: 24 Issue: 8 Pages: 164-176
  • DOI: 10.1090/ecgd/353
  • NAID: 120007165527
  • Peer Reviewed / Open Access
• [Journal Article] Hereditarily non uniformly perfect non-autonomous Julia sets (2020)
  • Author(s): Comerford Mark、Stankewitz Rich、Sumi Hiroki
  • Journal Title: Discrete & Continuous Dynamical Systems - A Volume: 40 Issue: 1 Pages: 33-46
  • DOI: 10.3934/dcds.2020002
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] The Hausdorff dimension function of the family of conformal iterated function systems of generalized complex continued fractions (2020)
  • Author(s): Inui Kanji、Okada Hikaru、Sumi Hiroki
  • Journal Title: Discrete & Continuous Dynamical Systems - A Volume: 40 Issue: 2 Pages: 753-766
  • DOI: 10.3934/dcds.2020060
  • Peer Reviewed
• [Journal Article] Hausdorff measures and packing measures of limit sets of CIFSs of generalized complex continued fractions (2020)
  • Author(s): Inui Kanji、Sumi Hiroki
  • Journal Title: Journal of Difference Equations and Applications Volume: 26 Issue: 1 Pages: 104-121
  • DOI: 10.1080/10236198.2019.1709063
  • Peer Reviewed
• [Journal Article] Spectral Gap Property for Random Dynamics on the Real Line and Multifractal Analysis of Generalised Takagi Functions (2020)
  • Author(s): Jaerisch Johannes、Sumi Hiroki
  • Journal Title: Communications in Mathematical Physics Volume: 377 Issue: 1 Pages: 1-36
  • DOI: 10.1007/s00220-020-03766-5
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Permutations uniquely identify states and unknown external forces in non-autonomous dynamical systems (2020)
  • Author(s): Hirata Yoshito、Sato Yuzuru、Faranda Davide
  • Journal Title: Chaos: An Interdisciplinary Journal of Nonlinear Science Volume: 30 Issue: 10 Pages: 103103-103103
  • DOI: 10.1063/5.0009450
  • NAID: 120007182859
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Automorphism groups of rational surfaces (2020)
  • Author(s): Uehara Takato
  • Journal Title: Journal of Pure and Applied Algebra Volume: 224 Issue: 1 Pages: 411-422
  • DOI: 10.1016/j.jpaa.2019.05.013
  • NAID: 120007034440
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Non-i.i.d. random holomorphic dynamical systems and the probability of tending to infinity (2019)
  • Author(s): Sumi Hiroki、Watanabe Takayuki
  • Journal Title: Nonlinearity Volume: 32 Issue: 10 Pages: 3742-3771
  • DOI: 10.1088/1361-6544/ab231e
  • Peer Reviewed
• [Journal Article] Anomalous Diffusion in Random Dynamical Systems (2019)
  • Author(s): Sato Yuzuru、Klages Rainer
  • Journal Title: Physical Review Letters Volume: 122 Issue: 17 Pages: 174101-174101
  • DOI: 10.1103/physrevlett.122.174101
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Minimal dynamical systems model of the Northern Hemisphere jet stream via embedding of climate data (2019)
  • Author(s): Faranda Davide、Sato Yuzuru、Messori Gabriele、Moloney Nicholas R.、Yiou Pascal
  • Journal Title: Earth System Dynamics Volume: 10 Issue: 3 Pages: 555-567
  • DOI: 10.5194/esd-10-555-2019
  • Peer Reviewed / Int'l Joint Research
• [Presentation] Two-dimensional random relaxed Newton's methods (2024)
  • Author(s): 角大輝
  • Organizer: 研究集 会「ランダム力学系とエルゴード理論」
• [Presentation] Multifractal analysis of growth rates for the geodesic flow on hyperbolic surfaces (2024)
  • Author(s): Johannes Jaerisch
  • Organizer: 2023年度 拡大版「リーマン面・不連続群論」研究集会
  • Invited
• [Presentation] Semigroups whose Julia sets are Cantor targets (2024)
  • Author(s): 諸澤俊介
  • Organizer: 拡大版「リーマン面・不連続群論」研究集会
• [Presentation] Dynamical spectrum on projective surfaces (2024)
  • Author(s): Takato Uehara
  • Organizer: Workshop on Dynamics in Arithmetic and Complex Geometry and its Applications
  • Invited
• [Presentation] Dynamical degrees of birational mappings on projective surfaces (2024)
  • Author(s): Takato Uehara
  • Organizer: 晴ればれ岡山代数幾何学シンポジウム
  • Invited
• [Presentation] On the dynamical spectrum on projective surfaces (2024)
  • Author(s): Takato Uehara
  • Organizer: 佐賀大学ワークショップ
  • Invited
• [Presentation] 穴あきトーラス群とそのタイヒミュラー空間について (2024)
  • Author(s): 中西敏浩
  • Organizer: リーマン面・不連続群論研究集会
• [Presentation] Anomalous diffusion and intermittency in random dynamical systems (2024)
  • Author(s): 佐藤譲
  • Organizer: ランダム力学系とエルゴード理論
  • Invited
• [Presentation] Random Dynamical Systems of Polynomial Automorphisms on \Bbb{C}^{2} (2023)
  • Author(s): Hiroki SUMI
  • Organizer: RIMS 総合研究セミナー「Mathematics of Random Systems: Summer School 2023」
  • Int'l Joint Research / Invited
• [Presentation] Complex two dimensional random relaxed Newton's methods (2023)
  • Author(s): Hiroki SUMI
  • Organizer: ICIAM 2023
  • Int'l Joint Research
• [Presentation] Multifractal analysis of growth rates for the geodesic flow on hyperbolic surfaces (2023)
  • Author(s): Johannes Jaerisch
  • Organizer: Dynamical Systems Seminar, University North Texas
  • Invited
• [Presentation] Growth rates and amenability for the geodesic flow on hyperbolic surfaces (2023)
  • Author(s): Johannes Jaerisch
  • Organizer: KiPAS Dynamics Days 2023
  • Invited
• [Presentation] On dynamical degrees of birational mappings (2023)
  • Author(s): Takato Uehara
  • Organizer: French-Japanese Workshop of Real and Complex Dynamics
  • Int'l Joint Research / Invited
• [Presentation] Fundamental regions for a Kleinian group (2023)
  • Author(s): Toshihiro Nakanishi
  • Organizer: Topology and Geometry of Low Dimensional Manifolds
  • Invited
• [Presentation] Stochastic chaos in random dynamical systems (2023)
  • Author(s): Yuzuru Sato
  • Organizer: Dynamics Days Kagurazaka
  • Invited
• [Presentation] Random Dynamical Systems of Polynomial Automorphisms on \Bbb{C}^{2} (2023)
  • Author(s): Hiroki SUMI
  • Organizer: The 10th Visegrad Conference on Dynamical Systems
  • Int'l Joint Research / Invited
• [Presentation] Random Dynamical Systems of Polynomial Automorphisms on \Bbb{C}^{2} (2023)
  • Author(s): Hiroki SUMI
  • Organizer: RIMS 共同研究「Around the Mandelbrot set」
  • Int'l Joint Research / Invited
• [Presentation] Multifractal analysis for the geodesic flow on hyperbolic surfaces (2023)
  • Author(s): Johannes Jaerisch
  • Organizer: Dynamics of (Semi-)Group Actions
  • Int'l Joint Research / Invited
• [Presentation] Stochastic chaos in random dynamical systems (2023)
  • Author(s): Yuzuru Sato
  • Organizer: International workshop on applied mathematics
• [Presentation] Anomalous diffusion and intermittency in random dynamical systems (2023)
  • Author(s): Yuzuru Sato
  • Organizer: Kipas Dynamics Days
  • Invited
• [Presentation] おもに種数２の閉曲面のタイヒミュラー空間とクライン群について (2023)
  • Author(s): 中西敏浩
  • Organizer: 日本数学会年会(特別講演）
  • Invited
• [Presentation] Random relaxed Newton's methods (2022)
  • Author(s): Hiroki SUMI
  • Organizer: RIMS 共同研究「ラン ダム力学系・非自励力学系研究の展望：理論と応用」
• [Presentation] Random Dynamical Systems of Polynomial Automorphisms on \Bbb{C}^{2} (2022)
  • Author(s): Hiroki SUMI
  • Organizer: RIMS 共同研究「複素力学系と関連分野」
  • Invited
• [Presentation] On a gluing construction of K3 surfaces (2022)
  • Author(s): Takato Uehara
  • Organizer: 2022年度城崎代数幾何学シンポジウム
  • Invited
• [Presentation] On dynamical degrees of birational mappings (2022)
  • Author(s): Takato Uehara
  • Organizer: RIMS Workshop Complex Dynamics and Related Topics
  • Invited
• [Presentation] Random Dynamical Systems of Regular Polynomial Maps on $\Bbb{C}^{2}$ (2022)
  • Author(s): Hiroki Sumi
  • Organizer: Dynamical systems and systems of equations
  • Int'l Joint Research / Invited
• [Presentation] Random Dynamical Systems of Regular Polynomial Maps on $\Bbb{C}^{2}$ (2022)
  • Author(s): Hiroki Sumi
  • Organizer: The 7th International Conference on Random Dynamical Systems
  • Int'l Joint Research / Invited
• [Presentation] Random relaxed Newton's methods (2022)
  • Author(s): 角大輝
  • Organizer: RIMS共同研究「ランダム力学系・非自励力学系研究の展望：理論と応用」
• [Presentation] Random Dynamical Systems of Polynomial Automorphisms on $\Bbb{C}^{2}$ (2022)
  • Author(s): 角大輝
  • Organizer: RIMS共同研究「複素力学系と関連分野」
  • Int'l Joint Research / Invited
• [Presentation] On dynamical degrees of birational mappings (2022)
  • Author(s): Takato Uehara
  • Organizer: RIMS共同研究「複素力学系と関連分野」
  • Int'l Joint Research / Invited
• [Presentation] 円周上の曲面束である３次元閉双曲多様体の具体例について (2022)
  • Author(s): 中西敏浩
  • Organizer: 東工大複素解析セミナー
  • Invited
• [Presentation] 2つ穴あきトーラスのTeichmuller空間とKlein群 (2022)
  • Author(s): 中西敏浩
  • Organizer: 愛媛大学解析セミナー
  • Invited
• [Presentation] Dynamical system of a sequence of inner composite functions (2022)
  • Author(s): 諸澤 俊介
  • Organizer: RIMS共同研究「複素力学系と関連分野」
  • Int'l Joint Research / Invited
• [Presentation] Multifractal analysis of the geodesic flow on hyperbolic surfaces (2022)
  • Author(s): Johannes Jaerisch
  • Organizer: RIMS共同研究「複素力学系と関連分野」
  • Int'l Joint Research / Invited
• [Presentation] Nonlinear stochastic phenomena in random dynamical systems (2022)
  • Author(s): Yuzuru Sato
  • Organizer: Hokkaido Summer Institute "Introduction to computational ergodic theory"
  • Int'l Joint Research
• [Presentation] Stochastic chaos in random dynamical systems (2022)
  • Author(s): Yuzuru Sato
  • Organizer: RIMS共同研究「ランダム力学系・非自励力学系研究の展望：理論と応用」
• [Presentation] Minimal dynamical systems model of the Northern Hemisphere jet stream via embedding of climate data (2022)
  • Author(s): Yuzuru Sato
  • Organizer: RIMS共同研究「ランダム力学系・非自励力学系研究の展望：理論と応用」
• [Presentation] Multifractal analysis of homological growth rates for hyperbolic surfaces (2022)
  • Author(s): Johannes Jaerisch and Hiroki Takahasi
  • Organizer: 2021年度 冬の力学系研究集会
• [Presentation] Random Dynamical Systems of Regular Polynomial Maps on $\Bbb{C}^{2}$ (2021)
  • Author(s): 角大輝
  • Organizer: RIMS共同研究「ランダム力学系および多価写像力学系理論の総合的研究」
• [Presentation] Random Dynamical Systems of Regular Polynomial Maps on $\Bbb{C}^{2}$ (2021)
  • Author(s): 角大輝
  • Organizer: RIMS共同研究「複素力学系の諸相」
  • Invited
• [Presentation] Random Dynamical Systems of Regular Polynomial Maps on C^{2} (2021)
  • Author(s): H. Sumi
  • Organizer: Dynamics of (Semi-)Group Actions
  • Int'l Joint Research / Invited
• [Presentation] Weighted cogrowth formula for free groups (2021)
  • Author(s): Johannes Jaerisch and Katsuhiko Matsuzaki
  • Organizer: エルゴード理論とその周辺
  • Int'l Joint Research
• [Presentation] Cusp winding spectra for some hyperbolic surfaces (2021)
  • Author(s): Johannes Jaerisch and Hiroki Takahasi
  • Organizer: 日本数学会秋季総合分科会
• [Presentation] Hausdorff dimension of escaping sets for Z extensions of expanding interval maps (2021)
  • Author(s): Johannes Jaerisch, Marc Kesseboehmer, Maik Groeger
  • Organizer: Dynamics of Semigroup actions
  • Int'l Joint Research / Invited
• [Presentation] Random Dynamical Systems of Regular Polynomial Maps on $\Bbb{C}^{2}$ (2021)
  • Author(s): Hiroki Sumi
  • Organizer: Dynamics of (Semi-)Group Actions
  • Int'l Joint Research / Invited
• [Presentation] Random Dynamical Systems of Regular Polynomial Maps on $\Bbb{C}^{2}$ (2021)
  • Author(s): 角大輝
  • Organizer: 数理解析研究所共同研究「ランダム力学系および多価写像力学系理論の総合的研究」
• [Presentation] Random Dynamical Systems of Regular Polynomial Maps on $\Bbb{C}^{2}$ (2021)
  • Author(s): 角大輝
  • Organizer: 数理解析研究所共同研究「複素力学系の諸相」
  • Invited
• [Presentation] Stochastic chaos in random dynamical systems and its Applications (2021)
  • Author(s): 佐藤譲
  • Organizer: Mathematical Science of Complex Systems: Physics, Chemistry, Biology, Information and Chaos
  • Invited
• [Presentation] Stochastic bifurcation in a turbulent swirling flow (2021)
  • Author(s): 佐藤譲
  • Organizer: RIMS workshop on dynamical systems
• [Presentation] Stochastic bifurcation in a turbulent swirling flow (2021)
  • Author(s): 佐藤譲
  • Organizer: Mathematical methods for the studies of flow, shape, and dynamics
  • Invited
• [Presentation] Existence of multiple noise-induced transitions in Lasota-Mackey map (2021)
  • Author(s): 佐藤譲
  • Organizer: Hokkaido Summer Institute on Computational Ergodic Theory
• [Presentation] いくつかのクライン群の例について (2021)
  • Author(s): 中西敏浩
  • Organizer: Workshop on Potential Theory and Complex Analysis
  • Invited
• [Presentation] 種数２の閉曲面のタイヒミュラー空間とクライン群の例について (2021)
  • Author(s): 中西敏浩
  • Organizer: 函数論シンポジウム
  • Invited
• [Presentation] Multifractal analysis of Birkhoff averages for non-uniformly expanding Markov interval maps (2021)
  • Author(s): Johannes Jaerisch and Hiroki Takahasi
  • Organizer: Ergodic theory and dynamical systems seminar of Tata Institute,
  • Int'l Joint Research / Invited
• [Presentation] Weighted cogrowth formula for free groups (2021)
  • Author(s): Johannes Jaerisch and Katsuhiko Matsuzaki
  • Organizer: Ergodic theory meeting, エルゴード理論とその周辺
  • Int'l Joint Research
• [Presentation] Cusp winding spectra for some hyperbolic surfaces (2021)
  • Author(s): Johannes Jaerisch and Hiroki Takahasi
  • Organizer: MSJ Autumn meeting
• [Presentation] Mixed Birkhoff spectra of one-dimensional Markov maps (2021)
  • Author(s): Johannes Jaerisch and Hiroki Takahasi
  • Organizer: MSJ Spring Meeting, Statistics and Probability Session
• [Presentation] A gluing construction of projective K3 surfaces (2021)
  • Author(s): Takato Uehara
  • Organizer: Aspects of Complex Dynamics
  • Int'l Joint Research / Invited
• [Presentation] ２つおよび３つの相似変換による相似タイリング (2021)
  • Author(s): 和田昌昭
  • Organizer: ランダム力学系および多価写像力学系理論の総合的研究
  • Invited
• [Presentation] Twisted Alexander 多項式の想い出 (2021)
  • Author(s): 和田昌昭
  • Organizer: トポロジーとコンピュータ2021
  • Invited
• [Presentation] Non-uniformly perfect Julia sets of non-autonomous dynamics of unbounded sequences of polynomials (2020)
  • Author(s): 角大輝
  • Organizer: 2019年度冬の力学系研究集会
• [Presentation] ランダム複素力学系における様々なランダム性誘起現象とそのメカニズム（日本数学会解析学賞受賞特別講演） (2020)
  • Author(s): 角大輝
  • Organizer: 2020年度日本数学会秋季総合分科会
  • Invited
• [Presentation] Non-uniformly perfect Julia sets of non-autonomous dynamics of unbounded sequences of polynomials (2020)
  • Author(s): 角大輝
  • Organizer: 数理解析研究所共同研究（公開型）「複素力学系理論の総合的研究」
  • Invited
• [Presentation] Stochastic bifurcation in a turbulent swirling flow (2020)
  • Author(s): 佐藤譲
  • Organizer: CRITICS workshop 2020
  • Int'l Joint Research / Invited
• [Presentation] Noise-induced degeneration in online learning (2020)
  • Author(s): 佐藤譲
  • Organizer: Dynamical systems and machine learning
  • Int'l Joint Research
• [Presentation] Multifractal analysis of Birkhoff averages for non-uniformly expanding Markov interval maps (2020)
  • Author(s): Johannes Jaerisch and Hiroki Takahasi
  • Organizer: Kyoto Dynamics Seminar
  • Invited
• [Presentation] Multifractal analysis of cuspidal windings on hyperbolic surfaces (2020)
  • Author(s): ohannes Jaerisch
  • Organizer: RIMS Online Workshop “Complex Dynamics and Related Topics
  • Invited
• [Presentation] Mixed Birkhoff spectra of one-dimensional Markov maps (2020)
  • Author(s): Johannes Jaerisch and Hiroki Takahasi
  • Organizer: RIMS 研究集会「数理科学の諸問題と力学系理論の新展開」
• [Presentation] Multifractal analysis of dynamical systems (2020)
  • Author(s): Johannes Jaerisch
  • Organizer: 名古屋大学談話会
  • Invited
• [Presentation] On maximal entropy measures for birational maps on compact complex surfaces (2020)
  • Author(s): Takato Uehara
  • Organizer: Complex Dynamics and Related Topics
  • Int'l Joint Research / Invited
• [Presentation] 2つおよび3つの相似変換による相似タイリング (2020)
  • Author(s): 和田昌昭
  • Organizer: トポロジーとコンピュータ2020
  • Invited
• [Presentation] Classification of generic random holomorphic dynamical systems associated with analytic families of rational maps (2019)
  • Author(s): Hiroki Sumi
  • Organizer: Thermodynamic Formalism; Applications to Geometry, Number Theory, and Stochastics
  • Int'l Joint Research / Invited
• [Presentation] Classification of generic random holomorphic dynamical systems associated with analytic families of rational maps (2019)
  • Author(s): Hiroki Sumi
  • Organizer: The 2019 Fall Program of Low-Dimensional Dynamics, Shanghai Center for Mathematical Sciences
  • Int'l Joint Research / Invited
• [Presentation] Classification of generic random holomorphic dynamical systems associated with analytic families of rational maps (2019)
  • Author(s): Hiroki Sumi
  • Organizer: 数理解析研究所研究集会「ランダム力学系理論とフラクタル幾何学の研究」
  • Int'l Joint Research
• [Presentation] Classification of generic random holomorphic dynamical systems associated with analytic families of rational maps (2019)
  • Author(s): 角大輝
  • Organizer: 第９回岐阜数理科学研究会
  • Invited
• [Presentation] Classification of generic random holomorphic dynamical systems associated with analytic families of rational maps (2019)
  • Author(s): 角大輝
  • Organizer: 研究集会「エルゴード理論とその周辺」
• [Presentation] Random holomorphic dynamical systems associated with analytic families of holomorphic maps (2019)
  • Author(s): 角大輝
  • Organizer: 数理解析研究所研究集会「複素力学系の分岐と安定性の研究」
  • Invited
• [Presentation] Anomalous diffusion in random dynamical systems (2019)
  • Author(s): 佐藤譲
  • Organizer: DCP19, CNR
  • Int'l Joint Research / Invited
• [Presentation] Stochastic bifurcation in a turbulent swirling flow (2019)
  • Author(s): 佐藤譲
  • Organizer: LML summer school, ICTP
  • Int'l Joint Research / Invited
• [Presentation] Stochastic bifurcation in a turbulent swirling flow (2019)
  • Author(s): 佐藤譲
  • Organizer: ICIAM
  • Int'l Joint Research / Invited
• [Presentation] Noise-induced Statistical Periodicity in Lasota-Mackey Maps (2019)
  • Author(s): 佐藤譲
  • Organizer: 数理解析研究所研究集会「ランダム力学系理論とフラクタル幾何学の研究」
  • Int'l Joint Research / Invited
• [Presentation] Anomalous diffusion and intermittency in deterministic /random dynamical systems (2019)
  • Author(s): 佐藤譲
  • Organizer: RIMSworkshop
  • Invited
• [Presentation] Stochastic bifurcation in a turbulent swirling flow (2019)
  • Author(s): 佐藤譲
  • Organizer: JSIAM
• [Presentation] Stochastic bifurcation and intermittency in random dynamical systems (2019)
  • Author(s): 佐藤譲
  • Organizer: RIMS workshop
• [Presentation] Anomalous diffusion in random dynamical systems (2019)
  • Author(s): 佐藤譲
  • Organizer: The Mathematics of Climate and Environment, IHP
  • Int'l Joint Research / Invited
• [Presentation] Anomalous diffusion in random dynamical systems (2019)
  • Author(s): 佐藤譲
  • Organizer: Shiga summer school
• [Presentation] Dimension gaps in transient dynamics on the real line (2019)
  • Author(s): Johannes Jaerisch
  • Organizer: 力学系-新たな理論と応用に向けて
  • Int'l Joint Research
• [Presentation] Spectral gap property for random dynamics on the real line and multifractal analysis of generalised Takagi functions (2019)
  • Author(s): Johannes Jaerisch
  • Organizer: Research on the Theory of Random Dynamical Systems and Fractal Geometry,
  • Int'l Joint Research
• [Presentation] Multifractal formalism for generalised local dimension spectra of Gibbs measures on the real line (2019)
  • Author(s): Johannes Jaerisch
  • Organizer: 2019年度日本数学会秋季総合分科会
• [Presentation] Recurrent and transient sets for skew-periodic interval maps (2019)
  • Author(s): Johannes Jaerisch
  • Organizer: エルゴード理論とその周辺
• [Presentation] Siegel disks for rational surface automorphisms with positive entropy (2019)
  • Author(s): Takato Uehara
  • Organizer: Geometric Complex Analysis on Foliations and Dynamics
  • Int'l Joint Research / Invited
• [Presentation] A gluing construction of K3 surfaces (2019)
  • Author(s): Takato Uehara
  • Organizer: Differential Systems: from theory to computer mathematics
  • Int'l Joint Research / Invited
• [Presentation] Dynamical degrees of birational maps on complex surfaces (2019)
  • Author(s): Takato Uehara
  • Organizer: Bifurcation and stability in complex dynamics
  • Int'l Joint Research / Invited
• [Presentation] Projective Hausdorff measure (2019)
  • Author(s): Masaaki Wada
  • Organizer: Research on the Theory of Random Dynamical Systems and Fractal Geometry
  • Int'l Joint Research / Invited
• [Presentation] Projective Hausdorff measure (2019)
  • Author(s): 和田昌昭
  • Organizer: Topology and Computer 2019
  • Int'l Joint Research / Invited
• [Book] 数理科学 -離散数理モデル- (2021)
  • Author(s): 石崎克也・諸澤俊介
  • Total Pages: 229
  • Publisher: NHK出版
  • ISBN: 9784595140587
• [Funded Workshop] RIMS 共同研究「Around the Mandelbrot set」 (2023)
• [Funded Workshop] 数理解析研究所共同研究（公開型）「ランダム力学系理論とフラクタル幾何学の研究」 (2019)