Open Access
Article
Shadowing Property on Finitely Generated Group Actions
Ali Barzanounia.barzanouni@hsu.ac.irDepartment of Mathematics, Hakim Sabzevari University E-mail:Sabzevar, IranView full profile →
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- Received:
- 19 Feb 2014
- Accepted:
- 12 Apr 2014
- Published Online:
- 02 Jan 2014
- Article type:
- Article
- Language:
- EN
- Article no.:
- 1726037X.2014.922253
- Pages:
- 69–79
Abstract
In this paper, we study shadowing property for actions of finitely generated groups and show that conjugacy preserves shadowing property and in the actions with shadowing property, topologically transitive is equivalent to chain transitive and the set of non-wandering points is equal to the set of chain recurrent points. For actions of finitely generated free groups, we prove that on a compact metric space of non-zero dimension, every action with chain transitive and shadowing property is sensitive.
Keywords
Subject Classifications
: 37C5037B05
References
JosephAuslander, Minimal flows and their extensions , North-Holland mathematics studies , 153 ( 1930 ). StevenHurder, Affine Anosov actions . The Michigan Mathematical Journal , Vol. 40 , Issue 3 , 419 - 618 ( 1993 ) SubrahmonianMoothathu, Implications of pseudo-orbit tracing property for continuous maps on compacta , Topology and its Applications 158 , 2232 - 2239 ( 2011 ) Alexey V.Osipov, Sergey B.Tikhomirov, Shadowing for actions of some finitely generated groups , preprint (arxiv.org/abs/1305.7394) .
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