2021 Fiscal Year Final Research Report
On the structure and the bifurcation of non-hyperbolic attracting regions: theory and numerics
| Project/Area Number |
18K03357
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Review Section |
Basic Section 12020:Mathematical analysis-related
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| Research Institution | Hitotsubashi University |
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Principal Investigator |
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| Project Period (FY) |
2018-04-01 – 2022-03-31
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| Keywords | 非双曲型力学系 / 野生的力学系 / ヘテロ次元サイクル / ホモクリニック接触 |
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| Outline of Final Research Achievements |
The structure and bifurcation theory of differential dynamical systems called non-hyperbolic dynamical systems, especially those of the type called absorbing domains, are studied from both theoretical and numerical viewpoints. Theoretical results showing that non-hyperbolic dynamical systems exhibit very complicated bifurcation phenomena (related to the super-exponential increase of periodic orbits and volume hyperbolicity and wildness) are obtained, and a methodology for the investigation of the structure called a blender, which is an important mechanism of the birth of non-hyperbolic dynamical systems, by using numerical analysis methods is proposed. The research results were published in four papers.
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| Free Research Field |
微分力学系
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| Academic Significance and Societal Importance of the Research Achievements |
微分力学系の知見はそれ自体が離散数理モデルや微分方程式の定性的理解の基礎となるものである．従って，本研究の結果は数理モデルを用いる現代の諸科学，ひいてはこれに立脚する現代社会に盤石な基礎を与えるものであると言えよう．本研究で扱った非双曲型力学系と呼ばれる種類の力学系は理論的に未知の部分が多い対象であり，今回の研究を通じて得られた理論的・数値解析的結果は今後様々な分野への知見を提供し，様々な波及効果を生むことが期待できる．
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