2018 Fiscal Year Final Research Report
Study of diffeomorphisms on geometric 3-manifolds
| Project/Area Number |
26400093
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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 | Tokyo Metropolitan University |
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Principal Investigator |
Soma Teruhiko 首都大学東京, 理学研究科, 教授 (50154688)
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| Co-Investigator(Kenkyū-buntansha) |
今井 淳 千葉大学, 大学院理学研究院, 教授 (70221132)
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| Project Period (FY) |
2014-04-01 – 2019-03-31
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| Keywords | 3-manifold / dynamical systems / diffeomorphism |
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| Outline of Final Research Achievements |
The main aim of this research project is to study structures of diffeomorphisms on 3-dimensional manifolds. To accomplish it, we investigated 2 and 3-dimensional diffeomorphisms from dynamical point of view. In fact we have obtained some new results on the existence of wandering domains including the affirmative answer of F. Takens conjecture. This is a research concerning on the complexity of orbits. This shows theoretically that it is often impossible to predict the orbits from statistical point of view.
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| Free Research Field |
位相幾何学
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| Academic Significance and Societal Importance of the Research Achievements |
この研究は，純粋に数学的な見地からの研究であるが，ある種の運動している物体の軌道を推測することが難しいことを理論的に説明してるとも言える．
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