Title: Cantor minimal models for ergodic transformations and topological orbit equivalence.
Speaker: Professor Isaac Kornfeld
Speaker Info: Northwestern University
According to a remarkable result of R. Jewett and W. Krieger, every ergodic automorphism of a nonatomic probability space admits a topological representation as a uniquely ergodic and minimal homeomorphism of a Cantor set. We will discuss a problem of constructing (simultaneous) topological models for families of ergodic transformations (instead of individual transformations), using Cantor minimal, non-uniquely ergodic systems. Even in very special cases, say, for the the family consisting of two irrational rotations of a circle, this question is nontrivial and has been unanswered until recently. It turns out that this question has positive answer for arbitrary finite or countable family of ergodic automorphisms. Moreover, the necessary representation can be found within the topological orbit equivalence class of any Cantor minimal system having sufficiently many invariant measures (joint work with N. Ormes). Some related questions, including variations on the theme of Lyapunov theorem on vector measures, will also be briefly discussed.Date: Tuesday, May 09, 2006