On m-minimal partially hyperbolic diffeomorphisms
Dynamical Systems
2015-12-02 v1
Abstract
We discuss about the denseness of the strong stable and unstable manifolds of partially hyperbolic diffeomorphisms. In this sense, we introduce a concept of m-minimality. More precisely, we say that a partially hyperbolic diffeomorphisms is m-minimal if m-almost every point in M has its strong stable and unstable manifolds dense in M. We show that this property has dynamics consequences: topological and ergodic. Also, we prove the abundance of m-minimal partially hyperbolic diffeomorphisms in the volume preserving and symplectic scenario.
Cite
@article{arxiv.1512.00388,
title = {On m-minimal partially hyperbolic diffeomorphisms},
author = {Alexander Arbieto and Thiago Catalan and Felipe Nobili},
journal= {arXiv preprint arXiv:1512.00388},
year = {2015}
}