Partially hyperbolic diffeomorphisms homotopic to the identity in dimension 3, Part II: Branching foliations
Abstract
We study -dimensional partially hyperbolic diffeomorphisms that are homotopic to the identity, focusing on the geometry and dynamics of Burago and Ivanov's center stable and center unstable \emph{branching} foliations. This extends our study of the true foliations that appear in the dynamically coherent case (see \emph{Partially hyperbolic diffeomorphisms homotopic to the identity in dimension 3, Part I: The dynamically coherent case}, arxiv:1908.06227v3). We complete the classification of such diffeomorphisms in Seifert fibered manifolds. In hyperbolic manifolds, we show that any such diffeomorphism is either dynamically coherent and has a power that is a discretized Anosov flow, or is of a new potential class called a \emph{double translation}.
Keywords
Cite
@article{arxiv.2008.04871,
title = {Partially hyperbolic diffeomorphisms homotopic to the identity in dimension 3, Part II: Branching foliations},
author = {Thomas Barthelmé and Sergio R. Fenley and Steven Frankel and Rafael Potrie},
journal= {arXiv preprint arXiv:2008.04871},
year = {2023}
}
Comments
This is the second part of arxiv:1908.06227v1 that was split in two. This version has a new part 2-specific introduction and some improved explanations in the text. v2: This is the final accepted version. Some improvements in the text thanks to referees reports