Horizontality of partially hyperbolic foliations

Fuente: arXiv
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Auteurs principaux: Hammerlindl, Andy, Potrie, Rafael
Format: Preprint
Publié: 2025
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author Hammerlindl, Andy
Potrie, Rafael
author_facet Hammerlindl, Andy
Potrie, Rafael
contents We show exactly which Seifert manifolds support partially hyperbolic dynamical systems. In particular, a circle bundle over a higher-genus surface supports a partially hyperbolic system if and only if it supports an Anosov flow. We also show for these systems that the center-stable and center-unstable foliations can be isotoped so that their leaves are transverse to the circle fibering. As a consequence, every partially hyperbolic system defined on the unit tangent bundle of a higher-genus surface is a collapsed Anosov flow.
format Preprint
id arxiv_https___arxiv_org_abs_2503_08077
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Horizontality of partially hyperbolic foliations
Hammerlindl, Andy
Potrie, Rafael
Dynamical Systems
37D30, 37C86, 57R30
We show exactly which Seifert manifolds support partially hyperbolic dynamical systems. In particular, a circle bundle over a higher-genus surface supports a partially hyperbolic system if and only if it supports an Anosov flow. We also show for these systems that the center-stable and center-unstable foliations can be isotoped so that their leaves are transverse to the circle fibering. As a consequence, every partially hyperbolic system defined on the unit tangent bundle of a higher-genus surface is a collapsed Anosov flow.
title Horizontality of partially hyperbolic foliations
topic Dynamical Systems
37D30, 37C86, 57R30
url https://arxiv.org/abs/2503.08077