Pseudo-orbit tracing and algebraic actions of countable amenable groups

DOI10.1017/etds.2017.126zbMath1431.37030arXiv1701.01318OpenAlexW2574602088MaRDI QIDQ5227743

Tom Meyerovitch

Publication date: 7 August 2019

Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1701.01318

zbMATH Keywords

topological entropygroup actionamenable groupcompact metric spacealgebraic actionpseudo-orbit tracingasymptotic pairexpansive action

Mathematics Subject Classification ID

Ergodic theory on groups (22D40) 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) Automorphisms, homomorphisms, endomorphisms, etc. for abelian groups (20K30)

Related Items (14)

Shadowing and mixing on systems of countable group actions ⋮ Garden of Eden and weakly periodic points for certain expansive actions of groups ⋮ Expansive actions with specification of sofic groups, strong topological Markov property, and surjunctivity ⋮ Gromov-Hausdorff distances for dynamical systems ⋮ On linear non-uniform cellular automata: duality and dynamics ⋮ Groups and dynamics: topology, measure, and Borel structure. Abstracts from the workshop held January 16--22, 2022 ⋮ Recoding Lie algebraic subshifts ⋮ Scale pressure for amenable group actions ⋮ A hierarchy of topological systems with completely positive entropy ⋮ Shadowing for families of endomorphisms of generalized group shifts ⋮ Markovian properties of continuous group actions: algebraic actions, entropy and the homoclinic group ⋮ Nilpotent endomorphisms of expansive group actions ⋮ Extracting invariants of conjugacy from independence entropy ⋮ The Lanford–Ruelle theorem for actions of sofic groups

Cites Work

• Unnamed Item
• Unnamed Item
• Representations of toral automorphisms
• Every transformation is bilaterally deterministic
• The cohomology of higher-dimensional shifts of finite type
• Homoclinic groups, IE groups, and expansive algebraic actions
• Symbolic dynamics on amenable groups: the entropy of generic shifts
• Automorphisms of compact groups
• Homoclinic points of algebraic $\mathbb {Z}^d$-actions
• Shadowing in multi-dimensional shift spaces
• Dynamical systems of algebraic origin
• Entropy theory from the orbital point of view

This page was built for publication: Pseudo-orbit tracing and algebraic actions of countable amenable groups