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TOPOLOGICAL STABILITY AND PSEUDO-ORBIT TRACING PROPERTY OF GROUP ACTIONS.
- Source :
-
Proceedings of the American Mathematical Society . Mar2018, Vol. 146 Issue 3, p1047-1057. 11p. - Publication Year :
- 2018
-
Abstract
- In this paper we extend the concept of topological stability from homeomorphisms to group actions on compact metric spaces and prove that if an action of a finitely generated group is expansive and has the pseudoorbit tracing property, then it is topologicaly stable. This represents a group action version of P. Walter's stability theorem [Lecture Notes in Math., vol. 668, Springer, 1978, pp. 231-244]. Moreover we give a class of group actions with topological stability or pseudo-orbit tracing property. In particular, we establish a characterization of subshifts of finite type over finitely generated groups in terms of the pseudo-orbit tracing property. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00029939
- Volume :
- 146
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- Proceedings of the American Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 127634911
- Full Text :
- https://doi.org/10.1090/proc/13654