Study of chaotic dynamical systems by use of geometric topology
Project/Area Number |
22540065
|
Research Category |
Grant-in-Aid for Scientific Research (C)
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Allocation Type | Single-year Grants |
Section | 一般 |
Research Field |
Geometry
|
Research Institution | University of Tsukuba |
Principal Investigator |
KATO Hisao 筑波大学, 数理物質系, 教授 (70152733)
|
Project Period (FY) |
2010 – 2012
|
Project Status |
Completed (Fiscal Year 2012)
|
Budget Amount *help |
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2012: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2011: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2010: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
|
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 / 位相力学系 / フラクタル次元 / 幾何学的トポロジー / 彩色問題 / 拡大同相写像 / 位相次元 / box次元 / coloring / 拡大定数 / flow |
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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Report
(4 results)
Research Products
(26 results)