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arXiv · 1512.00388

On m-minimal partially hyperbolic diffeomorphisms

Alexander Arbieto·Thiago Catalan·Felipe Nobili
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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.

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Alexander Arbieto, Thiago Catalan, Felipe Nobili. 2015-12-01. On m-minimal partially hyperbolic diffeomorphisms. https://arxiv.org/abs/1512.00388

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