Tel Aviv University Dear all, This week at the Horowitz seminar on Probability, Ergodic Theory and Dynamical Systems at Tel Aviv University we are happy to have: Speaker: Omri Sarig, Weizmann Institute and Pennsylvania State University Title: Symbolic dynamics for C^{1+epsilon} surface diffeomorphisms with positive topological entropy Date: Monday, March 21 Time: 14:30 Place: Schreiber 309 Abstract: Suppose f:M -->M is a C^{1+epsilon} diffeomorphism of a compact smooth manifold of dimension two with topological entropy h>0. For every 0<delta<h, we construct a "delta-large" invariant set E such that f restricted to E has a countable Markov partition. It follows that f|E is a finite-to-one factor of a topological Markov shift. "Delta-large" means that E has full measure for every ergodic invariant measure with entropy bigger than delta. There are many consequences, for example -- every ergodic measure of maximal entropy is a finite-to-one factor of a positive recurrent countable Markov chain, and is therefore isomorphic to a Bernoulli scheme times a rotation. Best regards, Ron Seminar webpage: <http://www.math.tau.ac.il/~peledron/Horowitz_seminar/Horowitz_seminar.html> --------------------------------------------------------- Technion Math Net-2 (TECHMATH2) Editor: Michael Cwikel <techm@math.technion.ac.il> Announcement from: Ron Peled <peledron@gmail.com>