On m-minimal partially hyperbolic diffeomorphisms

TL;DR

This paper introduces the concept of m-minimality for partially hyperbolic diffeomorphisms, showing that it implies significant dynamical consequences and is abundant in volume-preserving and symplectic cases.

Contribution

It defines m-minimality for partially hyperbolic diffeomorphisms and demonstrates its implications and abundance in specific dynamical contexts.

Findings

m-minimality implies topological and ergodic properties

m-minimal diffeomorphisms are abundant in volume-preserving cases

The concept links dense stable/unstable manifolds to dynamical behavior

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.