# Partial hyperbolicity and pseudo-Anosov dynamics

@inproceedings{Fenley2021PartialHA, title={Partial hyperbolicity and pseudo-Anosov dynamics}, author={S{\'e}rgio R. Fenley and R. Potrie}, year={2021} }

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 3manifolds 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.

## 3 Citations

### Collapsed Anosov flows and self orbit equivalences

- Mathematics
- 2020

We propose a generalization of the concept of discretized Anosov flows that covers a wide class of partially hyperbolic diffeomorphisms in 3-manifolds, and that we call collapsed Anosov flows. They…

### R-covered foliations and transverse pseudo-Anosov flows in atoroidal pieces

- Mathematics
- 2021

We study the transverse geometric behavior of 2-dimensional foliations in 3-manifolds. We show that an R-covered transversely orientable foliation with Gromov hyperbolic leaves in a closed 3-manifold…

### Minimality of the action on the universal circle of uniform foliations

- MathematicsGroups, Geometry, and Dynamics
- 2021

Given a uniform foliation by Gromov hyperbolic leaves on a $3$-manifold, we show that the action of the fundamental group on the universal circle is minimal and transitive on pairs of different…

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