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Horizontality of partially hyperbolic foliations

2025/03/11 by Andy Hammerlindl, Hammerlindl, Andy, Rafaël Potrie +1
Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Mathematics and Applications #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2503.08077

Abstract

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.

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