Illinois Journal of Mathematics

Expansive actions of countable amenable groups, homoclinic pairs, and the Myhill property

Tullio Ceccherini-Silberstein and Michel Coornaert

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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.

Article information

Illinois J. Math., Volume 59, Number 3 (2015), 597-621.

Received: 27 October 2015
Revised: 22 December 2015
First available in Project Euclid: 30 September 2016

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Zentralblatt MATH identifier

Primary: 37D20: Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) 37B40: Topological entropy 37B10: Symbolic dynamics [See also 37Cxx, 37Dxx] 43A07: Means on groups, semigroups, etc.; amenable groups


Ceccherini-Silberstein, Tullio; Coornaert, Michel. Expansive actions of countable amenable groups, homoclinic pairs, and the Myhill property. Illinois J. Math. 59 (2015), no. 3, 597--621. doi:10.1215/ijm/1475266399.

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