Shadowing for actions of some finitely generated groups

DOI10.1080/14689367.2014.902037zbMath1350.37030arXiv1305.7394OpenAlexW2146937148MaRDI QIDQ2875542

A. V. Osipov, Sergey B. Tikhomirov

Publication date: 8 August 2014

Published in: Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1305.7394

zbMATH Keywords

nilpotent groupfree groupgroup actionsolvable groupshadowingexpansivity

Mathematics Subject Classification ID

Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) (37D20) Dynamics induced by group actions other than (mathbb{Z}) and (mathbb{R}), and (mathbb{C}) (37C85) Dynamical systems involving transformations and group actions with special properties (minimality, distality, proximality, expansivity, etc.) (37B05)

Related Items (23)

Inverse shadowing in group actions ⋮ Shadowing and mixing on systems of countable group actions ⋮ Lipschitz structural stability of group actions with the shadowing property ⋮ Garden of Eden and weakly periodic points for certain expansive actions of groups ⋮ Shadowing property of 1-dimensional subsystems for suspension of \(\mathbb{Z}^k\)-actions ⋮ Gromov-Hausdorff distances for dynamical systems ⋮ Shadowing property of hyperspace for free semigroup actions ⋮ Rigidity of random group actions ⋮ Topological stability and shadowing property for group actions on metric spaces ⋮ Gromov-Hausdorff stability for group actions ⋮ Unnamed Item ⋮ Inverse shadowing in actions of a Baumslag-Solitar group ⋮ Shadowing property for the free group acting in the circle ⋮ Weak shadowing for actions of some finitely generated groups on non-compact spaces and related measures ⋮ Ergodic shadowing of semigroup actions ⋮ Shadowing for families of endomorphisms of generalized group shifts ⋮ The asymptotic average shadowing property of iterated function systems ⋮ Unnamed Item ⋮ Nilpotent endomorphisms of expansive group actions ⋮ C⁰-stability for actions implies shadowing property ⋮ On properties of expansive group actions ⋮ Topological stability and pseudo-orbit tracing property of group actions ⋮ Recurrent sets and shadowing for finitely generated semigroup actions on metric spaces

Cites Work

• Theory of pseudo-orbit shadowing in dynamical systems
• Shadowing with multidimensional time in Banach spaces
• Chain recurrence in multidimensional time discrete dynamical systems
• Expansive homeomorphisms with the pseudo-orbit tracing property on compact surfaces
• Groups of polynomial growth and expanding maps. Appendix by Jacques Tits
• Analogues of Takens theorems for generalized actions of the group \(\mathbb{Z}^\infty\)
• Algebraic Anosov actions of nilpotent Lie groups
• Generic properties of \(\mathbb Z^{2}\)-actions on the interval
• Shadowing vs. distality for actions of ℝⁿ
• Shadowing in actions of some Abelian groups
• Shadowing in multi-dimensional shift spaces

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