TY - JOUR

T1 - Shadowing for actions of some finitely generated groups

AU - Osipov, Alexey V.

AU - Tikhomirov, Sergey B.

PY - 2014

Y1 - 2014

N2 - 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.

AB - 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.

KW - shadowing

KW - expansivity

KW - group action

KW - nilpotent group

KW - solvable group

KW - free group

U2 - 10.1080/14689367.2014.902037

DO - 10.1080/14689367.2014.902037

M3 - Article

VL - 29

JO - Dynamical Systems

JF - Dynamical Systems

SN - 1468-9367

IS - 3

ER -