Time: 2018-11-05 10:30-12:00
For interval maps and surface diffeomorphisms, positive entropy is enough to generalize many properties of uniformly hyperbolic dynamics. Both systems can be represented by Markov shifts and build a spectral decomposition. One will show that this decomposition has finitely many pieces of large entropy and that each piece has a unique measure of maximal entropy. We will conclude by giving an almost Borel classification of these dynamics.