Transfer Operators Beyond Smooth or Uniformly Hyperbolic Systems

There has recently been an explosion of results about transfer operators acting on anisotropic Banach spaces, starting with correlation decay and the analyticity properties of the Ruelle dynamical zeta function of uniformly hyperbolic maps and flows. These techniques have been extended to hyperbolic systems withsingularities, but the results there are limited to low dimension and there is no access to zeta functions. They have also been exploited in nonuniformly hyperbolic systems even in infinite measure, but basically only in the Markov case. Finally, very few results are currently available regarding the application of these techniques to partially hyperbolic systems. This conference is devoted to exploring these ongoing developments.