Buzzi Jerome

I am mainly interest in entropy. My web page is here

As an organizer, I do not give a talk.

1. With respect to differentiable dynamics beyond uniform hyperbolicity, I am currently trying and understanding local constancy of the entropy that can occur… beyond uniform hyperbolicity. There are two joint works:

  • with Todd FISHER, Martin SAMBARINO, Carlos VASQUEZ to appear ETDS (partial, preprint version on arxiv)
  • with Todd FISHER, submitted (preprint version on arxiv

This should not be a generic situation as discussions with Crovisier confirm, at least in the C 1 situation. However, it remains to understand the boundary of this phenomenon.

Open Problem: Consider a diffeomorphism of compact d-dimensional manifold. Assume that d=u+s such that any smooth disk of dimension < u has entropy strictly less than that of f and likewise substituting (s,f^-1) to (u,f). Does it follow that the entropy of f is locally constant?

2. I am also interested in "nice generalizations" of subshifts of finite type which include interesting examples and yet keep most of the properties of the uniform case with respect to the measures of maximal entropy (see my old papers, A and B available on arxiv). There is an interesting recent preprint of Climenhaga and Thompson (see on arxiv).