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Emergence of differentiable dynamical systems with historic behavior

Research Project

Project/Area Number 18K03376
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Review Section Basic Section 12020:Mathematical analysis-related
Research InstitutionWaseda 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
Project Status Completed (Fiscal Year 2023)
Budget Amount *help
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2021: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2020: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2019: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2018: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Keywordsdiffeomorphism / Emergence / historic behavior / dynamical system / emergence / diffomorphism / Lyapunov exponent / homoclinic tangency / 力学系 / ヒストリー的挙動 / 創発性
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.

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.

Report

(7 results)
  • 2023 Annual Research Report   Final Research Report ( PDF )
  • 2022 Research-status Report
  • 2021 Research-status Report
  • 2020 Research-status Report
  • 2019 Research-status Report
  • 2018 Research-status Report
  • Research Products

    (12 results)

All 2023 2022 2020 2019 2018 Other

All Journal Article (6 results) (of which Int'l Joint Research: 2 results,  Peer Reviewed: 6 results) Book (1 results) Remarks (5 results)

  • [Journal Article] Observable Lyapunov irregular sets for planar piecewise expanding maps2023

    • Author(s)
      Y. Nakano Yushi, T. Soma, K. Yamamoto
    • Journal Title

      Discrete and Continuous Dynamical Systems

      Volume: 43 Issue: 7 Pages: 2737-2755

    • DOI

      10.3934/dcds.2023027

    • Related Report
      2022 Research-status Report
    • Peer Reviewed
  • [Journal Article] Abundance of Observable Lyapunov Irregular Sets2022

    • Author(s)
      Kiriki Shin、Li Xiaolong、Nakano Yushi、Soma Teruhiko
    • Journal Title

      Communications in Mathematical Physics

      Volume: 391 Issue: 3 Pages: 1241-1269

    • DOI

      10.1007/s00220-022-04337-6

    • Related Report
      2021 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Emergence via non-existence of averages2022

    • Author(s)
      Kiriki Shin、Nakano Yushi、Soma Teruhiko
    • Journal Title

      Advances in Mathematics

      Volume: 400 Pages: 108254-108254

    • DOI

      10.1016/j.aim.2022.108254

    • Related Report
      2021 Research-status Report
    • Peer Reviewed
  • [Journal Article] Historic behavior in nonhyperbolic homoclinic classes2019

    • Author(s)
      Barrientos Pablo G.、Kiriki Shin、Nakano Yushi、Raibekas Artem、Soma Teruhiko
    • Journal Title

      Proceedings of the American Mathematical Society

      Volume: 148 Issue: 3 Pages: 1195-1206

    • DOI

      10.1090/proc/14809

    • Related Report
      2019 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Historic behaviour for nonautonomous contraction mappings2019

    • Author(s)
      S. Kiriki, Y. Nakano and T. Soma
    • Journal Title

      Nonlinearity

      Volume: 32 Issue: 3 Pages: 1111-1124

    • DOI

      10.1088/1361-6544/aaf253

    • Related Report
      2018 Research-status Report
    • Peer Reviewed
  • [Journal Article] Moduli of 3-dimensional diffeomorphisms with saddle-foci2018

    • Author(s)
      Shinobu Hashimoto, Shin Kiriki, Teruhiko Soma
    • Journal Title

      Discrete & Continuous Dynamical Systems - A

      Volume: 38 Issue: 10 Pages: 5021-5037

    • DOI

      10.3934/dcds.2018220

    • Related Report
      2018 Research-status Report
    • Peer Reviewed
  • [Book] Geometry and topology of geometric limits I, In the Tradition of Thurston2020

    • Author(s)
      K. Ohshika and T. Soma
    • Total Pages
      73
    • Publisher
      Springer
    • Related Report
      2020 Research-status Report
  • [Remarks]

    • URL

      https://trhksoma.fpark.tmu.ac.jp/

    • Related Report
      2023 Annual Research Report
  • [Remarks]

    • URL

      https://www.comp.tmu.ac.jp/trhksoma/

    • Related Report
      2022 Research-status Report
  • [Remarks] Soma-index

    • URL

      http://www.comp.tmu.ac.jp/trhksoma/

    • Related Report
      2019 Research-status Report 2018 Research-status Report
  • [Remarks] Research map

    • URL

      https://researchmap.jp/read0027076/

    • Related Report
      2019 Research-status Report
  • [Remarks] 教員紹介 相馬 輝彦 | 首都大学東京

    • URL

      https://www.tmu.ac.jp/stafflist/data/sa/570.html

    • Related Report
      2018 Research-status Report

URL: 

Published: 2018-04-23   Modified: 2025-01-30  

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