2012 Fiscal Year Final Research Report
Study of chaotic dynamical systems by use of geometric topology
| Project/Area Number |
22540065
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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 | University of Tsukuba |
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Principal Investigator |
KATO Hisao 筑波大学, 数理物質系, 教授 (70152733)
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| Project Period (FY) |
2010 – 2012
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| Keywords | colorings / カオス / エントロピー / 拡大写像 / 連続体 / 非分解空間 / フラクタル |
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| Research Abstract |
We studied eventual colorings of maps. We obtained some important theorems of eventual coloring numbers. By use of Alexandroff-Urysohn metrization theorem we obtained very strong theorems concerning topological dimension and box-counting dimension. Also, we studied chaotic measure-preserving dynamical systems of compact manifolds. These results are very important in the theories of geometric topology and dynamical systems.
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