Dimensional entropies and semi-uniform hyperbolicity

Abstract

We describe dimensional entropies introduced in a previous work list some of their properties and give some new proofs. These entropies allowed the definition of entropy-expanding maps. We introduce a new notion of entropy-hyperbolicity for diffeomorphisms. We indicate some simple sufficient conditions (some of them new) for these properties. We conclude by some work in progress and more questions.

18 pages. To appear in Proc. Intern. Cong. Math. Phys., Rio, 2006