Shadowing for actions of some finitely generated groups.
Sergey Tikhomirov and Alexey Osipov
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Submission date: 30. Jan. 2014
published in: Dynamical systems : an international journal, 29 (2014) 3, p. 337-351
DOI number (of the published article): 10.1080/14689367.2014.902037
MSC-Numbers: 37C85, 37D20, 37C50
Keywords and phrases: Shadowing, expansivity, group action, nilpotent group, solvable group, free group
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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.