Partially hyperbolic diffeomorphisms with a trapping property

We study partially hyperbolic diffeomorphisms satisfying a trapping property which makes them look as if they were Anosov at large scale. We show that, as expected, they share several properties with Anosov diffeomorphisms. We construct an expansive quotient of the dynamics and study some dynamical consequences related to this quotient.Comment: 20 pages. New version incoporates improvements suggested by the refere

Many intermingled basins in dimension 3

We construct a diffeomorphism of $\mathbb{T}^3$ admitting any finite or countable number of physical measures with intermingled basins. The examples are partially hyperbolic with splitting $T\mathbb{T}^3 = E^{cs} \oplus E^u$ and can be made volume hyperbolic and topologically mixing.Comment: 20 pages, 4 figures. Some changes made after referee report. To appear in Israel J. of Mat