Characterizing sets of invariant probability measures of minimal homeomorphisms of the Cantor space

Abstract: Given a set K of probability measures on a Cantor set X, one can ask whether there exists a minimal homeomorphism (= all orbits are dense) whose invariant probability measures are exactly the elements of K. We say that K is a dynamical simplex if such a homeomorphism exists; I will present a characterization of dynamical simplices, which is based in large part on work of T. Ibarlucia and myself; and try to explain the proof strategy, based on the notion of Kakutani-Rokhlin partitions. The talk will be introductory in nature and not assume prior knowledge of Cantor dynamics.

dynamical systems

Audience: researchers in the topic

Dynamical systems seminar at the Jagiellonian University