Anomalous partially hyperbolic diffeomorphisms I: dynamically coherent\n examples

2014/11/05 by Christian Bonatti, Bonatti, Christian, Kamlesh Parwani +3
Mathematics · Physics and Astronomy · #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.1411.1221

openalex publication_date 2014/11/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We build an example of a non-transitive, dynamically coherent partially\nhyperbolic diffeomorphism f on a closed 3-manifold with exponential growth\nin its fundamental group such that fⁿ is not isotopic to the identity for\nall n\≠ 0. This example contradicts a conjecture in citeHHU. The main\nidea is to consider a well-understood time-t map of a non-transitive Anosov\nflow and then carefully compose with a Dehn twist.\n

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