Partially hyperbolic diffeormorphisms, ergodicity, and transverse foliations in dimension 3
Dynamical Systems
2025-10-20 v1 Geometric Topology
Abstract
We give a complete topological classification of transitive partially hyperbolic diffeomorphisms in 3-manifolds in terms of Anosov flows, completing a program proposed by Pujals. In particular, this also allows to give a full answer to the ergodicity conjecture of Hertz-Hertz-Ures for partially hyperbolic diffeomorphisms in dimension 3. This is achieved by showing a general result about pairs of transverse -dimensional foliations in 3-manifolds with Gromov hyperbolic leaves which may be of independent interest.
Cite
@article{arxiv.2510.15176,
title = {Partially hyperbolic diffeormorphisms, ergodicity, and transverse foliations in dimension 3},
author = {S. R. Fenley and R. Potrie},
journal= {arXiv preprint arXiv:2510.15176},
year = {2025}
}
Comments
57 pages, 16 figures