EXPANSIVE ACTIONS OF COUNTABLE AMENABLE GROUPS, HOMOCLINIC PAIRS, AND THE MYHILL PROPERTY

摘要

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 t: X → 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 τ then τ is surjective.