The Nonexistence of Expansive Z^d Actions on Graphs  

作　　者：En Hui SHI Li Zhen ZHOU 

机构地区：[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

出　　处：《Acta Mathematica Sinica,English Series》2005年第6期1509-1514,共6页数学学报（英文版）

基　　金：NSFC 10271085.K1107319

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.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：Expansive homeomorphism ARC Circle Group action 

分 类 号：O152[理学—数学]