Dynamics Beyond Uniform Hyperbolicity. A Global Geometric and Probabilistic Perspective

The notion of uniform hyperbolicity, introduced by Steve Smale in the early sixties, unified important developments, and led to a remarkably successful theory for a large class of systems: uniformly hyperbolic systems often exhibit complicated evolution which, nevertheless, is now rather well understood, both geometrically and statistically.

Another revolution has been taking place in the last couple of decades, as one tries to build a global theory for