2009 Fiscal Year Final Research Report
Study of dynamical and geometrical properties of maps on separable metric spaces
| Project/Area Number |
19540063
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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 University of Tsukuba, 大学院・数理物質科学研究科, 教授 (70152733)
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| Co-Investigator(Kenkyū-buntansha) |
SAKAI Katsuro 筑波大学, 大学院・数理物質科学研究科, 准教授 (50036084)
KAWAMURA Kazuhiro 筑波大学, 大学院・数理物質科学研究科, 准教授 (40204771)
KANETO Takeshi 筑波大学, 大学院・数理物質科学研究科, 講師 (70107340)
YAMAZAKI Kaori 高崎経済大学, 経済学部, 准教授 (80301076)
MINAMI Nariyuki 慶応義塾大学, 医学部, 教授 (10183964)
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| Project Period (FY) |
2007 – 2009
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| Keywords | 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 chaotic properties of maps of compact metric spaces by use of topological theory and ergodic theory. In this study, we proved that hereditarily indecomposable continua admit no expansive homeomorphisms. Also by use of Alexandroff-Urysohn metrization theorem we obtained very strong theorems concerning ratios of expanding maps and fractal dimensions. These results are very important in the theories of geometric topology and dynamical systems.
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