Analytic study of irrationally indifferent cycles in higher dimensional complex dynamics and non-archimedean dynamics

2019 Fiscal Year Final Research Report

• Project/Area Number: 15K04924
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Kyoto Institute of Technology
• Principal Investigator: OKUYAMA YUSUKE 京都工芸繊維大学, 基盤科学系, 教授 (00334954)
• Project Period (FY): 2015-04-01 – 2020-03-31
• Keywords: 複素力学系 / 非アルキメデス的力学系 / 無理的中立周期系

Outline of Final Research Achievements

We studied quantitatively the equidistribution phenomena towards the equilibirium measure and the approximation formula of the Lyapunov exponent with respect to the equilibrium measure from the view points of complex, non-archimedean, and arithmetic dynamics. In arithmetic dynamics, we obtained a quantitative estimate on the approximation of non-constant rational functions by dynamics on a singular domain associated to irrationally indifferent cycles.

Free Research Field

複素力学系、非アルキメデス的力学系

Academic Significance and Societal Importance of the Research Achievements

複素力学系や非アルキメデス的力学系においてはそのカオス部分が比較的具体的に解析することが可能であり、本研究はそれを進めてカオス部分を平衡測度を通じて定量的に解析していることに学術的意義があり、一般的なカオス現象の将来の解析の土台ともなり社会的意義もある。