The nonexistence of expansive Zd actions on graphs

被引：11
|
作者：
Shi, EH [1 ]
Zhou, LZ
机构：
[1] Univ Sci & Technol China, Dept Math, Hefei 230026, Peoples R China
[2] Suzhou Univ, Dept Math, Suzhou 215006, Peoples R China
来源：
ACTA MATHEMATICA SINICA-ENGLISH SERIES | 2005年 / 21卷 / 06期
关键词：
expansive homeomorphism; arc; circle; group action;
D O I：
10.1007/s10114-005-0640-3
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
It is well known that if X is an arc or a circle, then there is no expansive homeomorphism on X. In this paper we prove that there is no expansive Z(d) action on X, which answers the two questions raised by us before. In 1979, Mane proved that there is no expansive homeomorphism on infinite dimensional spaces. Contrary to this result, we construct an expansive Z(2) action on an infinite dimensional space. We also construct an expansive Z(2) action on a zero dimensional space but no element in Z(2) is expansive.
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页码：1509 / 1514
页数：6
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