Partial hyperbolicity and pseudo-Anosov dynamics

2021/02/03 by Fenley, Sergio R., Potrie, Rafael · 1 citation
#Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2102.02156

Abstract

We show that if a hyperbolic 3-manifold admits a partially hyperbolic diffeomorphism then it also admits an Anosov flow. Moreover, we give a complete classification of partially hyperbolic diffeomorphism in hyperbolic 3-manifolds as well as partially hyperbolic diffeomorphisms in Seifert manifolds inducing pseudo-Anosov dynamics in the base. This classification is given in terms of the structure of their center (branching) foliations and the notion of collapsed Anosov flows.

Cited by

• Partially hyperbolic diffeomorphisms homotopic to the identity in dimension three

Related

• Partially hyperbolic dynamics and 3-manifold topology
• Collapsed Anosov flows and self orbit equivalences
• Partially hyperbolic diffeomorphisms homotopic to the identity in dimension 3, Part I: The dynamically coherent case
• Partially hyperbolic diffeormorphisms, ergodicity, and transverse foliations in dimension 3
• Seifert manifolds admitting partially hyperbolic diffeomorphisms