Anomalous partially hyperbolic diffeomorphisms I: dynamically coherent examples

Abstract : We build an example of a non-transitive, dynamically coherent partially hyperbolic diffeomorphism $f$ on a closed 3-manifold with exponential growth in its fundamental group such that $f^n$ is not isotopic to the identity for all $n ≠ 0$. This example contradicts a conjecture in [F. RODRIGUEZ HERTZ, M. A. RODRIGUEZ HERTZ, R. URES, Partial hyperbolicity in 3-manifolds] The main idea is to consider a well-understood time-t map of a non-transitive Anosov ßow and then carefully compose with a Dehn twist.
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Contributeur : Imb - Université de Bourgogne <>
Soumis le : vendredi 3 mars 2017 - 17:46:35
Dernière modification le : jeudi 1 août 2019 - 13:34:02

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  • HAL Id : hal-01482732, version 1
  • ARXIV : 1411.1221


Christian Bonatti, Kamlesh Parwani,, Rafael Potrie. Anomalous partially hyperbolic diffeomorphisms I: dynamically coherent examples. Annales Scientifiques de l'École Normale Supérieure, Elsevier Masson, 2016, 49 (6), pp.1387-1402. ⟨hal-01482732⟩



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