Shadowing for actions of some finitely generated groups
- 6 March 2014
- journal article
- research article
- Published by Taylor & Francis Ltd in Dynamical Systems
- Vol. 29 (3), 337-351
- https://doi.org/10.1080/14689367.2014.902037
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.Keywords
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