Distorted diffeomorphisms and regularity.

ABSTRACT: The goal is to deal with the following question: for a compact manifold M, does there exist a diffeomorphism that is distorted in the group of C^r diffeomorphisms yet undistorted in the group of C^s diffeomorphism, where 1 \leq r < s ? Although the answer seems to be positive, it seems hard to build explicit examples (these diffeomorphisms necessarily have zero entropy). We will provide such examples for the closed unit interval for r = 1 and s = 2. The distortion part of the proof uses standard techniques on centralizers; the C^2 part uses recent work with Hélène Eynard on the relation between the Mather invariant and asymptotic distortion of 1-dimensional maps.

Posted on Jun 4, 2020 in Dynamical Systems, Seminars