2012 Fiscal Year Final Research Report
C2 robust heterodimensional tangencies on heterodimensional cycles
| Project/Area Number |
22540226
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Global analysis
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| Research Institution | Kyoto University of Education |
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Principal Investigator |
KIRIKI Shin 京都教育大学, 教育学部, 教授 (50277232)
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| Co-Investigator(Kenkyū-buntansha) |
SOMA Terhiko 首都大学東京, 理工学研究科, 教授 (50154688)
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| Project Period (FY) |
2010 – 2012
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| Keywords | 非双曲性 / ヘテロ次元サイクル / ホモクリニック分岐 |
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| Research Abstract |
We study diffeomorphisms having heterodimensional cycles containing a heterodimensional tangency. The main results of this study are the following:
(1) Arbitrarily close such a situation, we show existence of diffeomorphisms which have strange attractors
(2) and detect an open set of diffeomorphisms having C2 Newhouse phenomenon.
(3) Moreover, we show that such a critical cycle is robust in the C2 topology.
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