Partial hyperbolicity and pseudo-Anosov dynamics
Dynamical Systems
2024-01-23 v3 Geometric Topology
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.
Cite
@article{arxiv.2102.02156,
title = {Partial hyperbolicity and pseudo-Anosov dynamics},
author = {Sergio R. Fenley and Rafael Potrie},
journal= {arXiv preprint arXiv:2102.02156},
year = {2024}
}
Comments
66 pages, 9 figures. Some changes to take into accounts suggestions by a referee. To appear in GAFA