Historic behavior for non-trivial wandering domains: proof of Colli-Vargas' conjecture & answer to Takens' last problem)
Project/Area Number |
25400112
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Research Category |
Grant-in-Aid for Scientific Research (C)
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Allocation Type | Multi-year Fund |
Section | 一般 |
Research Field |
Basic analysis
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Research Institution | Tokai University |
Principal Investigator |
Kiriki Shin 東海大学, 理学部, 教授 (50277232)
|
Co-Investigator(Kenkyū-buntansha) |
相馬 輝彦 首都大学東京, 理工学研究科, 教授 (50154688)
|
Project Period (FY) |
2013-04-01 – 2017-03-31
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Project Status |
Completed (Fiscal Year 2016)
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Budget Amount *help |
¥4,940,000 (Direct Cost: ¥3,800,000、Indirect Cost: ¥1,140,000)
Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2014: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2013: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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Keywords | ホモクリニック分岐 / ヒストリック性 / エノン写像系 / 非双曲力学系 / 非自明遊走領域 / 双曲性 / 力学系 / Geometric Lorenz flow / Takens最終問題 / Colli-Vargas予想 / van Strien公開問題 / Colli-Vargasの予想 / vanStrienの公開問題 / Takensの最終公開問題 / 非自明な遊走集合 / Historic behavior / ホモクリニック接触 / wandering domain / homoclinic tangency / Takens' Last Problem / Colli-Vargas' conjecture / Henon map / トポロジー / 双曲力学系 / 遊走領域 |
Outline of Final Research Achievements |
We give an answer to a smooth version of the open problem of Takens in [Nonlinearity 21 (3) (2008) T33--T36.] which is related to historic behavior of dynamical systems. To obtain the answer, we show the existence of non-trivial wandering domains near a homoclinic tangency, which is conjectured by Colli-Vargas [Ergod. Th. Dynam. Sys. 21 (2001) 1657--1681]. Concretely speaking, it is proved that any Newhouse open set in the space of smooth diffeomorphisms on a closed surface is contained in the closure of the set of diffeomorphisms which have non-trivial wandering domains whose forward orbits have historic behavior. Moreover, this result implies an answer in the smooth category to one of the open problems of van Strien [Discrete Contin. Dyn. Syst. 27 (2) (2010) 557--588] which is concerned with wandering domains for Henon family.
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Report
(5 results)
Research Products
(24 results)