Emergence of differentiable dynamical systems with historic behavior

2023 Fiscal Year Final Research Report

• Project/Area Number: 18K03376
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Review Section: Basic Section 12020:Mathematical analysis-related
• Research Institution: Waseda University (2022-2023); Tokyo Metropolitan University (2018-2021)
• Principal Investigator: Soma Teruhiko 早稲田大学, 産業経営研究所, その他(招聘研究員) (50154688)
• Co-Investigator(Kenkyū-buntansha): 桐木 紳 東海大学, 理学部, 教授 (50277232) ; 中野 雄史 東海大学, 理学部, 准教授 (50778313)
• Project Period (FY): 2018-04-01 – 2024-03-31
• Keywords: diffeomorphism / Emergence / historic behavior

Outline of Final Research Achievements

The aim of this research project is to study emergence of diffeomorphisms. In particular, for diffeomorphisms on two-dimensional manifolds and some subsets of positive Lebesgue measure, our goal was to find a family of forward orbit based at points of the subset the emergency of which is Sup-P. The original plan has almost achieved and the result was published in an international journal. Through this research, it was found that the binary code corresponding to the orbit is more essential than diffeomorphism itself. So, we could prove that the above result holds for diffeomorphisms on manifolds of dimension 3 or more.

Free Research Field

Dynamical systems

Academic Significance and Societal Importance of the Research Achievements

本研究は，純粋に数学的な見地からの研究であるが，ある種の運動している物体の軌道を統計的に推測することにも関連している．それゆえ，応用数理的または物理学的検知からも有用な研究といえる．