2013 Fiscal Year Final Research Report
Flows and foliations subordinate to nonintegrable plane fields
| Project/Area Number |
23540071
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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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| Research Field |
Geometry
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| Research Institution | Chiba University |
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Principal Investigator |
INABA Takashi 千葉大学, 理学(系)研究科(研究院), 教授 (40125901)
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| Co-Investigator(Renkei-kenkyūsha) |
TSUBOI Takashi 東京大学, 大学院・数理科学研究科, 教授 (40114566)
NAKAYAMA Hiromichi 青山学院大学, 理工学部, 教授 (30227970)
KUGA Ken'ichi 千葉大学, 大学院・理学研究科, 教授 (30186374)
SUGIYAMA Ken-ichi 千葉大学, 大学院・理学研究科, 教授 (90206441)
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| Project Period (FY) |
2011 – 2013
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| Keywords | 微分トポロジー / 積分不可能平面場 / エントロピー |
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| Research Abstract |
1. Usual entropy always vanishes for nonintegrable plane fields (Zung 2011). We proposed a new definition of entropy which is involved in differentiability.
2. We introduced the concept of sensitive dependence on initial conditions (SDIC) for nonintegrable plane fields and constructed a nontrivial candidate for SDIC.
3. Given a contact manifold M and a torus T with a nonsingular flow, we constructed a contact form on M which defines the given contact structure and admits T as an invariant set of the associated Reeb flow.
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