2009 Fiscal Year Final Research Report
On rotation sets for angular velocity
| Project/Area Number |
19540090
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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 |
Geometry
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| Research Institution | Aoyama Gakuin University (2008-2009)
Hiroshima University (2007) |
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Principal Investigator |
NAKAYAMA Hiromichi Aoyama Gakuin University, 理工学部, 教授 (30227970)
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| Co-Investigator(Kenkyū-buntansha) |
MATSUMOTO Shigenori 日本大学, 理工学部, 教授 (80060143)
INABA Takashi 千葉大学, 理学研究科, 教授 (40125901)
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| Project Period (FY) |
2007 – 2009
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| Keywords | 微分トポロジー / 力学系 |
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| Research Abstract |
The purpose of this study is to find periodic orbits by examining the twist of the tangent vectors along the orbits. I showed the existence of periodic orbits from the velocity and the infinitesimal twist, and also classified connected minimal sets from the topological points of view. Furthermore I characterized the variation of angles along the orbits in minimal sets. As a main result, I proved the following theorem (a joint work with Shigenori Matsumoto) ; "Let f be an orientation preserving homeomorphism of the sphere which has a nontrivial continuum as a minimal set. Then there are exactly two invariant domains in the complement of the minimal set and all the other domains are wandering."
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