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Mathematics > Dynamical Systems
Title: Expansive actions with specification of sofic groups, strong topological Markov property, and surjunctivity
(Submitted on 26 Jul 2021 (v1), last revised 13 Sep 2022 (this version, v2))
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.
Submission history
From: Tullio Ceccherini-Silberstein [view email][v1] Mon, 26 Jul 2021 09:05:05 GMT (22kb)
[v2] Tue, 13 Sep 2022 10:07:54 GMT (24kb)
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