首页 | 本学科首页   官方微博 | 高级检索  
     检索      

The Nonexistence of Expansive Z^d Actions on Graphs
作者姓名:En  Hui  SHI  Li  Zhen  ZHOU
作者单位:[1]Department of Mathematics, University of Science and Technology of China, Hefei 230026, P. R. China [2]Department of Mathematics, Suzhou University, Suzhou 215006, P. R. China
基金项目:Supported by NSFC 10271085, K1-107319
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, Mané 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.

关 键 词:群论  同拓扑  扩展性    空间特性
收稿时间:2004-09-09
修稿时间:2004-09-092005-04-22

The Nonexistence of Expansive ℤ d Actions on Graphs
En Hui SHI Li Zhen ZHOU.The Nonexistence of Expansive Z^d Actions on Graphs[J].Acta Mathematica Sinica,2005,21(6):1509-1514.
Authors:En Hui Shi  Li Zhen Zhou
Institution:(1) Department of Mathematics, University of Science and Technology of China, Hefei 230026, P. R. China;(2) Department of Mathematics, Suzhou University, Suzhou 215006, P. R. China;(3) Department of Mathematics, Suzhou University, Suzhou 215006, P. R. China
Abstract: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 ? d action on X, which answers the two questions raised by us before. In 1979, Mañé proved that there is no expansive homeomorphism on infinite dimensional spaces. Contrary to this result, we construct an expansive ?2 action on an infinite dimensional space. We also construct an expansive ?2 action on a zero dimensional space but no element in ?2 is expansive.
Keywords:Expansive homeomorphism  Arc  Circle  Group action
本文献已被 维普 SpringerLink 等数据库收录!
设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号