Peter Hazards: Generic Properties of Hölder and Sobolev Homeomorphisms

A classical result (due to S. Ito and independently R. Bowen) states
that any biLipschitz homeomorphism on such spaces must always have
finite topological entropy.

Another, also classical, result (due to K. Yano) states that a generic
homeomorphism of a smooth compact manifold has infinite topological
entropy.

I will discuss current ongoing work, joint with E. de Faria and
C. Tresser, which describes what occurs in spaces of bi-Hölder and
bi-Sobolev homeomorphisms interpolating between these two scenarios.