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MiS Preprint
12/2014

Shadowing for actions of some finitely generated groups.

Sergey Tikhomirov and Alexey Osipov

Abstract

We introduce a notion of shadowing property for actions of finitely generated groups and study its basic properties. We formulate and prove a shadowing lemma for actions of nilpotent groups. We construct an example of a faithful linear action of a solvable Baumslag-Solitar group and show that the shadowing property depends on quantitative characteristics of hyperbolicity. Finally we show that any linear action of a non-abelian free group does not have the shadowing property.

Received:
Jan 30, 2014
Published:
Feb 11, 2014
MSC Codes:
37C85, 37D20, 37C50
Keywords:
Shadowing, expansivity, group action, nilpotent group, solvable group, free group

Related publications

inJournal
2014 Repository Open Access
Alexey Osipov and Sergey Tikhomirov

Shadowing for actions of some finitely generated groups

In: Dynamical systems : an international journal, 29 (2014) 3, pp. 337-351