"Geometry and Analysis on Groups" Research Seminar

Time:Nov 23, 11:00–12:00
Location: BZ02, Oskar-Morgenstern-Platz 1, 2.stock
Title: "Expansive actions of countable amenable groups, homoclinic pairs, and the Myhill property."
Speaker: Tullio Ceccherini-Silberstein (Università del Sannio)
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 $$\tau \colon\thinspace X \to X$$ 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. We also study the size of $$G$$–homoclinicity classes.

Joint work with Michel Coornaert.