Analytic studies of the moduli and irrationally indifferent cycles in higher dimensional complex and non-archimedean dynamics

2023 Fiscal Year Final Research Report

• Project/Area Number: 19K03541
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Review Section: Basic Section 12010:Basic analysis-related
• 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): 2019-04-01 – 2024-03-31
• Keywords: 複素力学系 / 非アルキメデス的力学系 / 算術力学系 / 無理的中立周期系 / モヂュライ

Outline of Final Research Achievements

We studied the dynamical moduli and their parabolic bifurcation loci in a quantitative way. Related to irrationally indifferent cycles in complex and non-archimedean dynamics, we studied the value distribution of morphisms into a Berkovich projective line around an isolated essential singularity, the equidistribution phenomena for the iterated pullbacks of points under any order derivatives of iterated polynomials, the equidistribution and the capacity of exceptional values for a family of morphisms and a marked point analitically parametrized by a Berkovich projective curve, the ergodic theory and equidistribution for quasiregular dynamics, the uniformly perfectness of Berkovich Julia sets, and a locally uniform a priori bound of the non-linearity on Berkovich Fatou sets.

Free Research Field

複素力学系、非アルキメデス的力学系、算術力学系

Academic Significance and Societal Importance of the Research Achievements

本研究は複素力学系や非アルキメデス的力学系におけるカオス部分およびそれら力学系のモヂュライにおける構造不安定部分を具体的かつ定量的に解析していることに学術的意義があり、より一般的なカオス現象の科学の土台ともなり社会的意義もある。