MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

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.

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