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Article Dans Une Revue Annales Scientifiques de l'École Normale Supérieure Année : 2016

Anomalous partially hyperbolic diffeomorphisms I: dynamically coherent examples

Résumé

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.

Dates et versions

hal-01482732 , version 1 (03-03-2017)

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