Fixed points and critical points in higher dimensional complex dynamics

• Project/Area Number: 21540176
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Kyoto University
• Principal Investigator: UEDA Tetsuo 京都大学, 理学(系)研究科(研究院), 教授 (10127053)
• Project Period (FY): 2009-04-01 – 2014-03-31
• Project Status: Completed (Fiscal Year 2013)
• Budget Amount: ¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000); Fiscal Year 2013: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000); Fiscal Year 2012: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000); Fiscal Year 2011: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000); Fiscal Year 2010: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000); Fiscal Year 2009: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
• Keywords: 複素力学系 / 放物型不動点 / ジュリア集合 / インプロージョン / 分岐点 / ファトゥ集合 / 放物型分岐点 / ファトウ集合

Research Abstract

I studied complex dynamics in higher dimension from the point of view of complex analysis of several complex variables. In particular, I investigated the phenomenon of implosion, i.e., the discontinuous change of (filled) Julia set that occur when a semi-parabolic and semi-attracting fixed point of a Henon mapping is perturbed. Also I investigated the dynamics of holomorphic self mappings of complex projective spaces. By tracking the orbit of the critical set, I obtained the condition for the set of repelling periodic points is dense in the projective space.

Research Products

• [Journal Article] Critically finite maps on projective spaces (II) (2011)
  • Author(s): Tetsuo Ueda
  • Journal Title: 数理解析研究所講究録 Volume: 1762 Pages: 120-124
  • Peer Reviewed
• [Presentation] Holomorphic maps on projective spaces and Fatou maps (2014)
  • Author(s): 上田哲生
  • Organizer: Moduli spaces and self-maps
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2014-03-06
• [Presentation] Dynamics of holomorphic maps in higher dimension (2014)
  • Author(s): 上田哲生
  • Organizer: Japan-Nepal Joint Workshop : Around higher dimensional complex systems
  • Place of Presentation: Kirtipur, Nepal
• [Presentation] 複素2次元半放物型不動点とその分岐 (2013)
  • Author(s): 上田哲生
  • Organizer: 日本数学会秋季総合分科会函数論分科会特別講演
  • Place of Presentation: 愛媛大学
  • Year and Date: 2013-09-13
• [Presentation] Semi-parabolic fixed points and their Bifurcations in complex dimension 2 (2013)
  • Author(s): 上田哲生
  • Organizer: Abel Symposium
  • Place of Presentation: Trondheim, Norway
  • Year and Date: 2013-07-02
• [Presentation] Semi-parabolic implosion in complex dimension 2,(Part 1) (2012)
  • Author(s): 上田哲生
  • Organizer: Interactions between continuous and discrete holomorphic dynamics
  • Place of Presentation: Banff International Research Station, Banff, Canada
  • Year and Date: 2012-07-11
• [Presentation] Parabolic Implosion in two complex variables (2012)
  • Author(s): 上田哲生
  • Organizer: 数理解析研究所研究集会「複素力学系の総合的研究」
  • Place of Presentation: 京都大学
  • Year and Date: 2012-01-25
• [Presentation] Semi-parabolic implosion in complex dimension 2 (2012)
  • Author(s): Tetsuo Ueda
  • Organizer: Interactions between continuous and discrete holomorphic dynamics
  • Place of Presentation: Banff, Canada
  • Invited
• [Presentation] Semi-parabolic implosion in complex dimension 2 (Part 1) (2011)
  • Author(s): 上田哲生
  • Organizer: 多変数関数論京都シンポジウムXIV
  • Place of Presentation: 京都大学
  • Year and Date: 2011-07-20
• [Presentation] Parabolic implosion in complex dimension 2 (2011)
  • Author(s): 上田哲生
  • Organizer: 第14回多変数函数論京都シンポジウム
  • Place of Presentation: 京都大学(招待講演)
  • Year and Date: 2011-07-20
• [Presentation] Critically finite maps on projective spaces (2010)
  • Author(s): 上田哲生
  • Organizer: 複素力学系とその周辺分野の研究
  • Year and Date: 2010-12-09
• [Presentation] Critically finite maps on projective spaces (2010)
  • Author(s): 上田哲生
  • Organizer: 数理解析研究所研究集会「複素力学系とその周辺分野の研究」
  • Place of Presentation: 京都大学
  • Year and Date: 2010-12-09
• [Presentation] Critically finite maps on projective spaces (2009)
  • Author(s): 上田哲生
  • Organizer: 多変数関数論冬セミナー
  • Place of Presentation: 岐阜大学
  • Year and Date: 2009-12-20
• [Presentation] Semi-parabolic fixed points and their bifurcations in complex dimension 2
  • Author(s): Tetsuo Ueda
  • Organizer: Abel Symposium
  • Place of Presentation: Trondheim, Norway
  • Invited