"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.