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Shadowing for actions of some finitely generated groups.
Sergey Tikhomirov and Alexey OsipovAbstract
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:
- 30.01.14
- Published:
- 11.02.14
- MSC Codes:
- 37C85, 37D20, 37C50
- Keywords:
- Shadowing, expansivity, group action, nilpotent group, solvable group, free group