Shadowing for actions of some finitely generated groups

被引：30

作者：

Osipov, Alexey V. ^{[1
,2
]}

Tikhomirov, Sergey B. ^{[1
,3
,4
]}

机构：

[1] St Petersburg State Univ, Dept Math & Mech, Chebyshev Lab, St Petersburg 199178, Russia

[2] Scuola Normale Super Pisa, Ctr Ric Matemat Ennio de Giorgi, I-56100 Pisa, Italy

[3] Free Univ Berlin, Inst Math 1, D-14195 Berlin, Germany

[4] Max Planck Inst Math Sci, D-04103 Leipzig, Germany

来源：

DYNAMICAL SYSTEMS-AN INTERNATIONAL JOURNAL | 2014年 / 29卷 / 03期

基金：

俄罗斯基础研究基金会;

关键词：

shadowing; expansivity; group action; nilpotent group; solvable group; free group; ORBIT-TRACING-PROPERTY; EXPANSIVE HOMEOMORPHISMS; MULTIDIMENSIONAL TIME;

D O I：

10.1080/14689367.2014.902037

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：337 / 351

页数：15

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