Laminations in complex dynamics generated by Zalcman's lemma

• Project/Area Number: 24740103
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Global analysis
• Research Institution: Tokyo Institute of Technology (2014-2015); Nagoya University (2012-2013)
• Principal Investigator: Kawahira Tomoki 東京工業大学, 理工学研究科, 准教授 (50377975)
• Project Period (FY): 2012-04-01 – 2016-03-31
• Project Status: Completed (Fiscal Year 2015)
• Budget Amount: ¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000); Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2012: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
• Keywords: 複素力学系 / ザルクマンの補題 / ラミネーション / 剛性 / Zalcmanの補題 / 力学系の剛性 / Mandelbrot集合 / Julia集合 / Tricorn / Julia 集合 / Teichmuller理論 / 国際情報交換 / タイヒミュラー理論

Outline of Final Research Achievements

A complex dynamics is a system where the complex numbers move according to a deterministic law of motion. We mainly considered the cases when the law of motion depends on a complex parameter. The system may be unstable under perturbation at some parameters and the set of such parameters often behaves like a chaotic locus of a given complex dynamics. In this research project, we choose "Zalcman's lemma" as a bridge that connects dynamical systems and the parameter spaces. Most of our results are related to the family of quadratic polynomials.

Research Products

• [Int'l Joint Research] Academia Sinica(台湾)
• [Journal Article] Quatre applications du lemme de Zalcman a la dynamique complexe (2014)
  • Author(s): Tomoki Kawahira
  • Journal Title: J.Anal.Math Volume: 124 Issue: 1 Pages: 309-334
  • DOI: 10.1007/s11854-014-0034-5
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Quatre application du lemme de Zalcman a la dynamique complexe (2014)
  • Author(s): T.Kawahira
  • Journal Title: J. Anal. Math. Volume: 未定
  • Peer Reviewed
• [Journal Article] On the natural extensions of dynamics with a Siegel or Cremer point (2012)
  • 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
  • Peer Reviewed
• [Presentation] From Cantor to Misiurewicz along parameter rays (2016)
  • Author(s): 川平友規
  • Organizer: 日本数学会
  • Place of Presentation: 筑波大学
  • Year and Date: 2016-03-16
• [Presentation] The Riemann hypothesis and holomorphic index in complex dynamics (2016)
  • Author(s): 川平友規
  • Organizer: 日本数学会
  • Place of Presentation: 筑波大学
  • Year and Date: 2016-03-16
• [Presentation] 複素力学系とリーマン予想，固定点の正則指数 (2016)
  • Author(s): 川平友規
  • Organizer: 冬の力学系研究集会
  • Place of Presentation: 日大軽井沢研修所
  • Year and Date: 2016-01-09
• [Presentation] The Riemann hypothesis and holomorphic index in complex dynamics (2015)
  • Author(s): 川平友規
  • Organizer: RIMS研究集会「複素力学系の深化」
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2015-12-09
  • Int'l Joint Research
• [Presentation] From Cantor to Misiurewicz along parameter ray (2015)
  • Author(s): 川平友規
  • Organizer: RIMS研究集会「複素力学系の深化」
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2015-12-08
  • Int'l Joint Research
• [Presentation] From Cantor to Misiurewicz along parameter rays (2015)
  • Author(s): 川平友規
  • Organizer: RIMS研究集会「力学系とその諸分野への応用」
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2015-07-02
  • Int'l Joint Research
• [Presentation] タイヒミュラー空間の基礎のキソ
  • Author(s): 川平 友規
  • Organizer: 第47回函数論サマーセミナー
  • Place of Presentation: かんぽの宿 鳥羽
  • Invited
• [Presentation] 双曲型Riemann面のTeichmuller空間と複素力学系
  • Author(s): 川平 友規
  • Organizer: 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
  • Invited
• [Presentation] On dynamical and parametric Zalcman functoins
  • Author(s): 川平 友規
  • Organizer: 2012年度複素力学系研究集会 -- 複素力学系の新展開 --
  • Place of Presentation: 京都大学
  • Invited
• [Presentation] Zalcmanの補題と複素力学系
  • Author(s): 川平 友規
  • Organizer: 2013年度日本数学会年会・函数論分科会
  • Place of Presentation: 京都大学
  • Invited
• [Book] レクチャーズ オン Mathematica (2013)
  • Author(s): 川平 友規
  • Total Pages: 196
  • Publisher: プレアデス出版
• [Remarks] 研究者本人のwebページ
  • URL: http://www.math.titech.ac.jp/~kawahira
• [Remarks] 研究者の研究・教育ページ
  • URL: http://www.math.titech.ac.jp/~kawahira
• [Remarks] 研究者web page
  • URL: http://www.math.nagoya-u.ac.jp/~kawahira
• [Remarks] http://www.math.nagoya-u.ac.jp/~kawahira