** "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.