The shadowing and topological stability properties of semigroup actions on non-compact metric spaces

Document Type : Original Paper

Authors

1 Department of Mathematics, Faculty of Mathematics, Statistics and Computer Science, University of Sistan and Baluchestan, Zahedan, Iran

2 Department of Mathematics, Faculty of Mathematics and Computer Science, Hakim Sabzevari University, Sabzevar, Iran

Abstract

‎In this paper, the concepts of shadowing, weak shadowing and expansiveness for finitely generated semigroup actions on non-compact metric spaces are introduced, which are dynamical properties and equivalent to their definitions on compact metric spaces. Also, the notion of topological stability for actions associated to finitely generated abelain semigroups is defined and a necessary and sufficient condition for the topological stability of finitely generated abelian semigroups on a locally compact metric space ‎is ‎provided.‎

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Main Subjects


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