Analytical studies of irrationally indifferent cycles in higher dimensional complex dynamics and Nevanlinna theory

• Project/Area Number: 21740096
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: Basic analysis
• Research Institution: Kyoto Institute of Technology
• Principal Investigator: OKUYAMA Yusuke 京都工芸繊維大学, 工芸科学研究科, 准教授 (00334954)
• Project Period (FY): 2009 – 2011
• Project Status: Completed (Fiscal Year 2011)
• Budget Amount: ¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000); Fiscal Year 2011: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2010: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000); Fiscal Year 2009: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
• Keywords: 複素力学系 / ネヴァンリンナ理論 / 無理的中立周期系

Research Abstract

We obtained the finiteness and vanishig of the nonlinearity of finite morphisms on projective space over more general fields than complex numbers, and applied it to singular domains in complex dynamics in higher dimensions. Moreover, under the positivity of Lyapunov exponents, we obtained a partial affirmative answer for repelling density problem in non-archimedean dynamics by establishing the approximation formula of Lyapunov exponents.

Research Products

• [Journal Article] Repelling periodic points and logarithmic equidistribution in non-archimedean dynamics (2012)
  • Author(s): Yusuke Okuyama
  • Journal Title: Acta Arith. Volume: 152, No.3 Pages: 267-277
  • Peer Reviewed
• [Journal Article] Potential theory and a characterization of polynomials in complex dynamics (2011)
  • Author(s): Yusuke Okuyama and Malgorzata Stawiska
  • Journal Title: Conform. Geom. Dyn. Volume: 15 Pages: 152-159
  • Peer Reviewed
• [Journal Article] Potential theory and a characterization of polynomials in complex dynamics (2011)
  • Author(s): Yusuke Okuyama, Malgorzata Stawiska
  • Journal Title: Conform.Geom.Dyn. Volume: 15 Issue: 10 Pages: 152-159
  • DOI: 10.1090/s1088-4173-2011-00230-x
  • Peer Reviewed
• [Journal Article] Nonlinearity of morphisms in non-archimedean and complex dynamic (2010)
  • Author(s): Yusuke Okuyama
  • Journal Title: Michigan Math J. Volume: 59, No.3 Pages: 505-515
  • Peer Reviewed
• [Journal Article] Nonlinearity of morphisms in non-Archimedean and complex dynamics (2010)
  • Author(s): Yusuke Okuyama
  • Journal Title: Michigan Mathematical Journal Volume: 59 Pages: 505-515
  • Peer Reviewed
• [Journal Article] singular domains in higher dimensional complex dynamics (2009)
  • Author(s): Yusuke Okuyama
  • Journal Title: 数理解析研究所講究録 1661 Pages: 99-103
• [Presentation] Diophantine approximation and quantitative equidistribution (2012)
  • Author(s): 奥山裕介
  • Organizer: 日本数学会2011年年会代数学分科会
  • Place of Presentation: 東京理科大学
  • Year and Date: 2012-03-29
• [Presentation] Repelling density problem and approximation of Lyapunov exponents (2012)
  • Author(s): 奥山裕介
  • Organizer: 日本数学会2011年年会代数学分科会
  • Place of Presentation: 東京理科大学
  • Year and Date: 2012-03-29
• [Presentation] Characterization of polynomials from potential theory and complex dynamics (2012)
  • Author(s): 奥山裕介
  • Organizer: 日本数学会2011年年会函数論分科会
  • Place of Presentation: 東京理科大学
  • Year and Date: 2012-03-26
• [Presentation] Convergence of multiplier heights to Lyapunov exponents in non-archimedean dynamics (2012)
  • Author(s): 奥山裕介
  • Organizer: HawaiConference in Algebraic Number Theory, Arithmetic Geometry, and Modular Forms, Arithmetic Geometry session
  • Place of Presentation: University of Hawai' i in Honolulu
  • Year and Date: 2012-03-07
• [Presentation] Convergence of multiplier heights to Lyapunov exponents in non-archimedean dynamics (2012)
  • Author(s): Yusuke Okuyama
  • Organizer: Hawai'i Conference in Algebraic Number Theory, Arithmetic Geometry, and Modular Forms
  • Place of Presentation: Univ.of Hawai'i (USA)(招待講演)
  • Year and Date: 2012-03-07
• [Presentation] Quantitative equidistribution in dynamics over general fields (2012)
  • Author(s): 奥山裕介
  • Organizer: AMS Spring 2012 Western Sectional, special session on "Arithmetic Geometry"
  • Place of Presentation: University of Hawai' i in Honolulu
  • Year and Date: 2012-03-03
• [Presentation] Quantitative equidistribution in dynamics over general fields (2012)
  • Author(s): Yusuke Okuyama
  • Organizer: AMS Spring 2012 Western Sectional, special session on "Arithmetic Geometry"
  • Place of Presentation: Univ.of Hawai'i (USA)(招待講演)
  • Year and Date: 2012-03-03
• [Presentation] Quantitative Equidistribution in Non-Archimedean and Complex Dyanmics (2012)
  • Author(s): 奥山裕介
  • Organizer: Complex and p-adic dynamics
  • Place of Presentation: Institute for Computational and Experimental Research in Mathematics(ICERM)
  • Year and Date: 2012-02-13
• [Presentation] Quantitative Equidistribution in Non-Archimedean and Complex Dyanmics (2012)
  • Author(s): Yusuke Okuyama
  • Organizer: Complex and p-adic dynamics in ICERM Semester Program on "Complex and Arithmetic Dynamics"
  • Place of Presentation: ICERM (USA)(招待講演)
  • Year and Date: 2012-02-13
• [Presentation] The density problem on repelling periodic points of non-archimedean rational functions (2012)
  • Author(s): 奥山裕介
  • Organizer: 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: 2012-01-24
• [Presentation] The repelling density problem and logarithmic equidistribution in non-archimedean and complex dynamics (2011)
  • Author(s): 奥山裕介
  • Organizer: The 19th International Conference on Finite or Infinite Dimensional Complex Analysis and Applications
  • Place of Presentation: Aster Plaza, Hiroshima
  • Year and Date: 2011-12-12
• [Presentation] The repelling density problem and logarithmic equidistribution in non-archimedean and complex dynamics (2011)
  • Author(s): Yusuke Okuyama
  • Organizer: The 19tn International Conference on Finite or Infinite Dimensional Complex Analysis and Applications
  • Place of Presentation: Aster Plaza, Hiroshima(日本)(招待講演)
  • Year and Date: 2011-12-12
• [Presentation] 非アラケロフ幾何的非アルキメデス力学系 (2011)
  • Author(s): 奥山裕介
  • Organizer: ポテンシャル論とファイバー空間
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2011-09-05
• [Presentation] Approximation of Lyapunov exponents and convergence of potentials in complex dynamics (2010)
  • Author(s): 奥山裕介
  • Organizer: Conference on complex analysis
  • Place of Presentation: University of Illinois at Urbana-Champaign
  • Year and Date: 2010-05-21
• [Presentation] 複素力学系とその周辺-非アルキメデス的力学系の非線型性、カオス性、数論性- (2009)
  • Author(s): 奥山裕介
  • 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
• [Presentation] (非)アルキメデス的力学系の非線型性と力学系への応用 (2009)
  • Author(s): 奥山裕介
  • Organizer: 日本数学会2009年秋季総合分科会函数論分科会
  • Place of Presentation: 大阪大学大学院理学研究科
  • Year and Date: 2009-09-26