Expansive Behaviours for Homeomorphisms of tvs-Cone Metric Spaces
Received:March 20, 2015  Revised:March 08, 2016
Key Words: tvs-cone metric space   tvs-cone expansive homeomorphism   generator   converging semiorbit  
Fund Project:Supported by the National Natural Science Foundation of China (Grant Nos.11301367; 61472469; 11461005) and the Doctoral Fund of Ministry of Education of China (Grant No.20123201120001).
Author NameAffiliation
Xun GE School of Mathematical Sciences, Soochow University, Jiangsu 215006, P. R. China 
Hits: 2300
Download times: 2070
Abstract:
      Let $f$ be a homeomorphism of a compact tvs-cone metric space. In this paper, we show that $f$ is tvs-cone expansive if and only if $f$ has a generator. Further, it is proved that if $f$ is tvs-cone expansive, then the set of points having converging semiorbits under $f$ is a countable set. Results of this paper improve some expansive homeomorphisms theorems in topological dynamics, which will help to research dynamical properties for homeomorphisms of tvs-cone metric spaces.
Citation:
DOI:10.3770/j.issn:2095-2651.2016.03.012
View Full Text  View/Add Comment