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MiS Preprint

Shadowing for actions of some finitely generated groups.

Sergey Tikhomirov and Alexey Osipov


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.

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

Related publications

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