Surjunctivity and topological rigidity of algebraic dynamical systems

Abstract

Let $X$ be a compact metrizable group and $\Gamma$ a countable group acting on $X$ by continuous group automorphisms. We give sufficient conditions under which the dynamical system $(X,\Gamma )$ is surjunctive, i.e., every injective continuous map $\tau :X\to X$ commuting with the action of $\Gamma$ is surjective.

arXiv admin note: text overlap with arXiv:1612.05893

References in corpus (2)

• Finite entropy characterizes topological rigidity
• Orbit equivalence and topological conjugacy of affine actions on compact abelian groups

Cited by in corpus (3)

• Markovian properties of continuous group actions: algebraic actions, entropy and the homoclinic group
• Expansive actions with specification of sofic groups, strong topological Markov property, and surjunctivity
• A Garden of Eden theorem for principal algebraic actions