2001 Fiscal Year Final Research Report Summary
Research of invariant sets of topological dynamics in continuum theory
| Project/Area Number |
11640058
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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, Institute of Mathematics, Professor, 数学系, 教授 (70152733)
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| Co-Investigator(Kenkyū-buntansha) |
KAWAMURA Kazuhiro University of Tsukuba, Institute of Mathematics, Associate Professor, 数学系, 助教授 (40204771)
SAKAI Katsuro University of Tsukuba, Institute of Mathematics, Associate Professor, 数学系, 助教授 (50036084)
HOSHINA Takao University of Tsukuba, Institute of Mathematics, Professor, 数学系, 教授 (00015893)
YAMAZAKI Kaori University of Tsukuba, Institute of Mathematics, Assistant, 数学系, 教授 (80301076)
KANETO Takeshi University of Tsukuba, Institute of Mathematics, Lecture, 数学系, 講師 (70107340)
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| Project Period (FY) |
1999 – 2001
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| Keywords | Chaos / chaos in the sense of Devaney and Li-Yorke / scrambled set / indecomposability / entropy / expansive homeomorphism / fractal set / Menger manifold |
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| Research Abstract |
We investigated some properties of invariant sets and minimal sets of expansive homeomorphisms and continuum-wise expansive homeomorphisms, which are important in Chaotic dynamical systems. In 1979, Mane proved that every minimal set of expansive homeomorphism is 0-dimensional, and the head investigator generalized this result concerning to continuum-wise expansive homeomorphism. In this rearch project, we proved that each continuum-wise expansive homeomorphism of 1-dimensional compactum admits many minimal sets which are Cantor sets. Also, every continuum-wise fully expansive homeomorphism homeomorphism admits many minimal sets which are Cantor sets. These rtesults imply that ( continuum-wise ) expansive homeomorphisms induce chaos of periodicity.
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Research Products
(12 results)
