Collapsed Anosov flows and self orbit equivalences
Abstract
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 are related with Anosov flows via a self orbit equivalence of the flow. We show that all the examples constructed in a paper by Bonatti, Gogolev, Hammerlindl and the third author belong to this class, and that it is an open and closed class among partially hyperbolic diffeomorphisms. We provide some equivalent definitions which may be more amenable to analysis and are useful in different situations. Conversely we describe the class of partially hyperbolic diffeomorphisms that are collapsed Anosov flows associated with certain types of Anosov flows.
Cite
@article{arxiv.2008.06547,
title = {Collapsed Anosov flows and self orbit equivalences},
author = {Thomas Barthelmé and Sergio R. Fenley and Rafael Potrie},
journal= {arXiv preprint arXiv:2008.06547},
year = {2022}
}
Comments
81 pages, 1 figure. This version clarifies some hypothesis and provides more details in some arguments. It also points out shortcuts to get some relevant instances of the results. Final version, to appear in Comm. Math. Helv