Partially hyperbolic diffeormorphisms, ergodicity, and transverse foliations in dimension 3

2025/10/16 by Sérgio R. Fenley, Fenley, S. R., Rafaël Potrie +1
Mathematics · Physics and Astronomy · #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.2510.15176

openalex publication_date 2025/10/16 · openalex created_date 2025/10/21 · openalex updated_date 2026/07/28

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 2-dimensional foliations in 3-manifolds with Gromov hyperbolic leaves which may be of independent interest.

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