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Shadowing for actions of some finitely generated groups. / Osipov, Alexey V.; Tikhomirov, Sergey B.

In: Dynamical Systems, Vol. 29, No. 3, 2014.

Research output: Contribution to journal › Article

Harvard

Osipov, AV & Tikhomirov, SB 2014, 'Shadowing for actions of some finitely generated groups', Dynamical Systems, vol. 29, no. 3. https://doi.org/10.1080/14689367.2014.902037

APA

Osipov, A. V., & Tikhomirov, S. B. (2014). Shadowing for actions of some finitely generated groups. Dynamical Systems, 29(3). https://doi.org/10.1080/14689367.2014.902037

Vancouver

Osipov AV, Tikhomirov SB. Shadowing for actions of some finitely generated groups. Dynamical Systems. 2014;29(3). https://doi.org/10.1080/14689367.2014.902037

Author

Osipov, Alexey V. ; Tikhomirov, Sergey B. / Shadowing for actions of some finitely generated groups. In: Dynamical Systems. 2014 ; Vol. 29, No. 3.

BibTeX

@article{9fb84048bcf14099841120cd2146facb,
title = "Shadowing for actions of some finitely generated groups",
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 = "shadowing, expansivity, group action, nilpotent group, solvable group, free group",
author = "Osipov, {Alexey V.} and Tikhomirov, {Sergey B.}",
year = "2014",
doi = "10.1080/14689367.2014.902037",
language = "English",
volume = "29",
journal = "Dynamical Systems",
issn = "1468-9367",
publisher = "Taylor & Francis",
number = "3",

}

RIS

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 -

ID: 7018595