2019 Fiscal Year Final Research Report
Bifurcation of chaotic dynamical systems
| Project/Area Number |
26287016
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Partial Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Kyoto University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
稲生 啓行 京都大学, 理学研究科, 准教授 (00362434)
上田 哲生 京都大学, 理学研究科, 名誉教授 (10127053)
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| Project Period (FY) |
2014-04-01 – 2020-03-31
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| Keywords | 力学系 / 分岐 / くりこみ / カオス / フラクタル |
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| Outline of Final Research Achievements |
Shishikura constructed a topological model for hedgehogs for irrationally indifferent fixed points by introducing the notion of dynamical charts, in order to apply the theory of near-parabolic renormalizations and its invariant spaces. Inou together with Mukherjee studied Tricorn family to prove non-landing properties of umbilical cords, except trivial cases. Shishikura together with David Marti Pete improved Bishop's quasiconformal folding techniques to show that there exists a transcendental entire function of finite order which has oscillating wandering domains.
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| Free Research Field |
力学系理論
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| Academic Significance and Societal Importance of the Research Achievements |
力学系は，低次元であっても，しばしば複雑で予測不可能な挙動（カオス）を示し、パラメータを変化させるとき，その様相を大きく変化させる。これを分岐現象と呼ぶ。再帰的軌道をもつ力学系の分岐パラメータの集合は入り組んだ階層的構造をもつ。本研究では、力学系の複素力学系の再帰的な軌道や放物型分岐の研究を中心に、それらがパラメータ空間の構造に及ぼす影響や再帰写像をとることによって得られるくりこみの理論の研究を行った。
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