Abstract
Let $X$ be a compact metrizable space equipped with a continuous action of a countable amenable group $G$. Suppose that the dynamical system $(X,G)$ is expansive and is the quotient by a uniformly bounded-to-one factor map of a strongly irreducible subshift. Let $\tau\colon X\to X$ be a continuous map commuting with the action of $G$. We prove that if there is no pair of distinct $G$-homoclinic points in $X$ having the same image under $\tau$ then $\tau$ is surjective.
Citation
Tullio Ceccherini-Silberstein. Michel Coornaert. "Expansive actions of countable amenable groups, homoclinic pairs, and the Myhill property." Illinois J. Math. 59 (3) 597 - 621, Fall 2015. https://doi.org/10.1215/ijm/1475266399
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