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

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. (c) 2024 Elsevier Inc. All rights reserved.