Expansive actions with specification of sofic groups, strong topological Markov property, and surjunctivity

Abstract

A dynamical system is a pair $(X,G)$, where $X$ is a compact metrizable space and $G$ is a countable group acting by homeomorphisms of $X$. An endomorphism of $(X,G)$ is a continuous selfmap of $X$ which commutes with the action of $G$. One says that a dynamical system $(X,G)$ is surjunctive provided that every injective endomorphism of $(X,G)$ is surjective (and therefore is a homeomorphism). We show that when $G$ is sofic, every expansive dynamical system $(X,G)$ with nonnegative sofic topological entropy and satisfying the weak specification and the strong topological Markov properties, is surjunctive.

This is a slightly revised and updated version

References in corpus (1)

• Markovian properties of continuous group actions: algebraic actions, entropy and the homoclinic group

Cited by in corpus (1)

• Homomorphisms from aperiodic subshifts to subshifts with the finite extension property