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Hyperbolic geometric approaches to rigidity problems in complex dynamics

Research Project

Project/Area Number 20740092
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeSingle-year Grants
Research Field Global analysis
Research InstitutionNagoya University

Principal Investigator

KAWAHIRA Tomoki  名古屋大学, 多元数理科学研究科, 准教授 (50377975)

Project Period (FY) 2008 – 2011
Project Status Completed (Fiscal Year 2011)
Budget Amount *help
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2010: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2009: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2008: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Keywords複素力学系 / 双曲的力学系の稠密性 / 剛性 / 双曲幾何 / ラミネーション / サリバンの辞書 / ザルクマンの補題
Research Abstract

A complex dynamics is a system where the complex numbers move according to a deterministic law of motion. When we perturb the law of motion, the system may be stable, or change in a chaotic way. However, it is known that "in most cases", such systems are stable. The aim of this research was to characterize such stable systems in a geometric approach.

Report

(6 results)
  • 2011 Annual Research Report   Final Research Report ( PDF )
  • 2010 Annual Research Report   Self-evaluation Report ( PDF )
  • 2009 Annual Research Report
  • 2008 Annual Research Report
  • Research Products

    (36 results)

All 2012 2011 2010 2009 2008 Other

All Journal Article (17 results) (of which Peer Reviewed: 14 results) Presentation (13 results) Remarks (6 results)

  • [Journal Article] On the natural extensions of dynamics with a Siegel or Cremer point2012

    • Author(s)
      C. Cabrera and T. Kawahira
    • Journal Title

      J. Diff. Equ. Appl

      Volume: 19 Issue: 5 Pages: 701-711

    • DOI

      10.1080/10236198.2012.681780

    • Related Report
      2011 Annual Research Report 2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Family of invariant Cantor sets as orbits of differential equations, II : Julia sets2011

    • Author(s)
      Y.-C. Chen, T. Kawahira, H-L Li, and J-M Yuan
    • Journal Title

      Inter. J. Bifur. & Chaos

      Volume: 21 Pages: 77-99

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Family of invariant Cantor sets as orbits of differential equations II : Julia sets.2011

    • Author(s)
      Y-C Chen, T.Kawahira, H-L Li, J-M Yuan
    • Journal Title

      Inter.J .Bifur.& Chaos. 21

      Pages: 77-99

    • Related Report
      2010 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] Family of invariant cantor sets as orbits of differential equations, II : Julia sets2011

    • Author(s)
      Y-C.Chen, T.Kawahira, H-L.Li, J-M.Yuan
    • Journal Title

      Inter.J.Bifur.& Chaos

      Volume: 21 Pages: 77-79

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Some new applications of Zalcman's lemma to complex dynamics2010

    • Author(s)
      T. Kawahira
    • Journal Title

      RIMS Kokyuroku

      Volume: 1699 Pages: 44-61

    • Related Report
      2011 Final Research Report
  • [Journal Article] Some new applications of Zalcman's lemma to complex dynamics.(In Japanese).2010

    • Author(s)
      T.Kawahira.
    • Journal Title

      RIMS Kokyuroku 1699

      Pages: 44-61

    • Related Report
      2010 Self-evaluation Report
  • [Journal Article] Topology of the regular part for infinitely renormalizable quadratic polynomials2009

    • Author(s)
      C. Cabrera and T. Kawahira
    • Journal Title

      Fund. Math

      Volume: 208 Pages: 35-56

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Tessellation and Lyubich-Minsky laminations associated with quadratic maps II : Topological structures of 3-laminations2009

    • Author(s)
      T. Kawahira
    • Journal Title

      Conformal Geom. Dyn

      Volume: 13 Pages: 6-75

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Tessellation and Lyubich-Minsky laminations associated with quadratic maps I : Pinching semiconjugacies2009

    • Author(s)
      T. Kawahira
    • Journal Title

      Ergodic Theory Dynam. Systems

      Volume: 29, no2 Pages: 579-612

    • NAID

      120002603244

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Topology of the regular part for infinitely renormalizable quadratic polynomials.2009

    • Author(s)
      C.Cabrera, T.Kawahira.
    • Journal Title

      Fund.Math. 208

      Pages: 35-56

    • Related Report
      2010 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] Tessellation and Lyubich-Minsky laminations associated with quadratic maps II: Topological structures of 3-laminations.2009

    • Author(s)
      T.Kawahira.
    • Journal Title

      Conformal Geom.Dyn. 13

      Pages: 6-75

    • Related Report
      2010 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] Tessellation and Lyubich-Minsky laminations associated with quadratic maps I : Pinching semiconjugacies.2009

    • Author(s)
      T.Kawahira.
    • Journal Title

      Ergodic Theory Dynam.Systems 29,no 2

      Pages: 579-612

    • NAID

      120002603244

    • Related Report
      2010 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] Topology of the regular part for infinitely renormalizable quadratic polynomials2009

    • Author(s)
      C.Cabrera, T.Kawahira
    • Journal Title

      Fund.Math. 208

      Pages: 35-56

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Tessellation and Lyubich-Minsky laminations associated with quadratic maps I : Pinching semiconjugacies2009

    • Author(s)
      Tomoki Kawahira
    • Journal Title

      Ergodic Th. & Dynam. Sys. 29

      Pages: 579-612

    • NAID

      120002603244

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Tessellation and Lyubich-Minsky laminations associated with quadratic maps II : Topological structures of 3-laminations2009

    • Author(s)
      Tomoki Kawahira
    • Journal Title

      Conform. Geom. Dynam. 13

      Pages: 6-75

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Rigidity of Riemann surface laminations associated with infinitely renormalizable quadratic maps2008

    • Author(s)
      Tomoki Kawahira
    • Journal Title

      数理解析研究所講究録 1586

      Pages: 160-168

    • Related Report
      2008 Annual Research Report
  • [Journal Article] Family of invariant cantor sets as orbits of differential equations, II : Julia sets

    • Author(s)
      Y-C.Chen, T.Kawahira, H-L.Li, J-M.Yuan
    • Journal Title

      Inter.J.Bifur.& Chaos (未定)(掲載決定済み)

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Presentation] Denseness of repelling cycles in the Julia set and its parameter analogue2012

    • Author(s)
      T. Kawahira
    • Organizer
      Complex and P-adic Dynamics Tutorial Week
    • Place of Presentation
      ICERM, Brown University, USA
    • Year and Date
      2012-02-09
    • Related Report
      2011 Final Research Report
  • [Presentation] 複素力学系から生成されるリーマン面ラミネーション2012

    • Author(s)
      川平友規
    • Organizer
      2011年度複素力学系研究集会-複素力学系の総合的研究-
    • Place of Presentation
      京都大学数理解析研究所420号室
    • Year and Date
      2012-01-26
    • Related Report
      2011 Final Research Report
  • [Presentation] 複素力学系から生成されるリーマン面ラミネーション2012

    • Author(s)
      川平友規
    • Organizer
      複素力学系研究集会--複素力学系の総合的研究--
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2012-01-26
    • Related Report
      2011 Annual Research Report
  • [Presentation] Zalcmanの補題が生成する複素力学系のリーマン面ラミネーション2011

    • Author(s)
      川平友規
    • Organizer
      研究集会「複素解析的ベクトル場・葉層構造とその周辺」
    • Place of Presentation
      龍谷大学セミナーハウスともいき荘
    • Year and Date
      2011-12-09
    • Related Report
      2011 Final Research Report
  • [Presentation] Some new applications of Zalcman's lemma to complex dynamics2009

    • Author(s)
      川平友規
    • Organizer
      RIMS研究集会「複素力学系とその関連分野の総合的研究」
    • Place of Presentation
      京都大学
    • Year and Date
      2009-12-15
    • Related Report
      2011 Final Research Report
  • [Presentation] Some new applications of Zalcman's lemma to complex dynamics.2009

    • Author(s)
      川平友規
    • Organizer
      RIMS研究集会「複素力学系とその関連分野の総合的研究」
    • Place of Presentation
      京都大学
    • Year and Date
      2009-12-15
    • Related Report
      2010 Self-evaluation Report
  • [Presentation] Zalcmanの補題:複素力学系への3つの応用2009

    • Author(s)
      川平友規
    • Organizer
      第52回函数論シンポジウム
    • Place of Presentation
      大阪府立大学
    • Year and Date
      2009-11-21
    • Related Report
      2011 Final Research Report 2010 Self-evaluation Report
  • [Presentation] Zalcmanの補題:複素力学系への3つの応用2009

    • Author(s)
      川平友規
    • Organizer
      第52回函数論シンポジウム
    • Place of Presentation
      大阪府立大
    • Year and Date
      2009-10-23
    • Related Report
      2009 Annual Research Report
  • [Presentation] 複素力学系理論からみたゼータ関数2008

    • Author(s)
      川平友規
    • Organizer
      共同研究企画「L関数の値分布と関係する数論的な諸関数の研究」
    • Place of Presentation
      京都大学
    • Year and Date
      2008-07-03
    • Related Report
      2011 Final Research Report
  • [Presentation] 複素力学系理論からみたゼータ関数共同研究企画2008

    • Author(s)
      川平友規
    • Organizer
      L関数の値分布と関係する数論的な諸関数の研究
    • Place of Presentation
      京都大学
    • Year and Date
      2008-07-03
    • Related Report
      2010 Self-evaluation Report
  • [Presentation] Topology of the Lyubich-Minsky lamination : Deformation and rigidity2008

    • Author(s)
      川平友規
    • Organizer
      Journe' es de Dynamique Complexe
    • Place of Presentation
      Universite' de Paris VI
    • Related Report
      2011 Final Research Report
  • [Presentation] Topology of the Lyubich-Minsky lamination : Deformation and rigidity.2008

    • Author(s)
      川平友規
    • Organizer
      Journe'es de Dynamique Complexe
    • Place of Presentation
      Universite' de Paris VI.
    • Related Report
      2010 Self-evaluation Report
  • [Presentation] Topology of the Lyubichr-Minskylamination : Deformation and rigidity2008

    • Author(s)
      Tomoki Kawahira
    • Organizer
      Journees de Dynamique Complexe
    • Place of Presentation
      Institut de Mathematique de Jussieu
    • Related Report
      2008 Annual Research Report
  • [Remarks] プレプリント: T. Kawahira. Quatre applications du lemme de Zalcman` a la dynamique complexe, Submitted, 2010.

    • URL

      http://www.math.nagoya-u.ac.jp/~kawahira

    • Related Report
      2011 Final Research Report
  • [Remarks]

    • URL

      http://www.math.nagoya-u.ac.jp/~kawahira

    • Related Report
      2011 Annual Research Report
  • [Remarks] ホームページ

    • URL

      http://www.math.nagoya-u.ac.jp/~kawahira

    • Related Report
      2010 Self-evaluation Report
  • [Remarks]

    • URL

      http://www.math.nagoya-u.ac.jp/~kawahira

    • Related Report
      2010 Annual Research Report
  • [Remarks]

    • URL

      http://www.math.nagoya-u.ac.jp/~kawahira

    • Related Report
      2009 Annual Research Report
  • [Remarks]

    • URL

      http://www.math.nagoya-u.ac.jp/~kawahira

    • Related Report
      2008 Annual Research Report

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Published: 2008-04-01   Modified: 2016-04-21  

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