Project/Area Number 
11640058

Research Category 
GrantinAid for Scientific Research (C)

Allocation Type  Singleyear Grants 
Section  一般 
Research Field 
Geometry

Research Institution  University of Tsukuba 
Principal Investigator 
KATO Hisao University of Tsukuba, Institute of Mathematics, Professor, 数学系, 教授 (70152733)

CoInvestigator(Kenkyūbuntansha) 
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)

Project Period (FY) 
1999 – 2001

Project Status 
Completed (Fiscal Year 2001)

Budget Amount *help 
¥3,700,000 (Direct Cost: ¥3,700,000)
Fiscal Year 2001: ¥1,100,000 (Direct Cost: ¥1,100,000)
Fiscal Year 2000: ¥1,100,000 (Direct Cost: ¥1,100,000)
Fiscal Year 1999: ¥1,500,000 (Direct Cost: ¥1,500,000)

Keywords  Chaos / chaos in the sense of Devaney and LiYorke / scrambled set / indecomposability / entropy / expansive homeomorphism / fractal set / Menger manifold / Devaney, LiYorkeのカオス / Devney,LiYorKeのカオス / 分解不可能性 / 測度不変同相写像 / ウィリアムスの予想 
Research Abstract 
We investigated some properties of invariant sets and minimal sets of expansive homeomorphisms and continuumwise expansive homeomorphisms, which are important in Chaotic dynamical systems. In 1979, Mane proved that every minimal set of expansive homeomorphism is 0dimensional, and the head investigator generalized this result concerning to continuumwise expansive homeomorphism. In this rearch project, we proved that each continuumwise expansive homeomorphism of 1dimensional compactum admits many minimal sets which are Cantor sets. Also, every continuumwise fully expansive homeomorphism homeomorphism admits many minimal sets which are Cantor sets. These rtesults imply that ( continuumwise ) expansive homeomorphisms induce chaos of periodicity.
