Partially hyperbolic diffeomorphisms with a trapping property

TL;DR

This paper investigates a class of partially hyperbolic diffeomorphisms with a trapping property, revealing their similarities to Anosov systems and exploring their expansive quotients and dynamical implications.

Contribution

It introduces a trapping property for partially hyperbolic diffeomorphisms and analyzes the resulting expansive quotient, extending understanding of their dynamical behavior.

Findings

Shared properties with Anosov diffeomorphisms

Construction of an expansive quotient

Dynamical consequences of the quotient

Abstract

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.