Anomalous partially hyperbolic diffeomorphisms I: dynamically coherent examples
[Difféomorphismes partiellement hyperboliques anormaux I: exemples dynamiquement cohérents]
Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 49 (2016) no. 6, pp. 1387-1402.

Sur une 3-variété fermée dont le groupe fondamental est à croissance exponentielle, nous construisons un exemple de difféomorphisme f, partiellement hyperbolique, dynamiquement cohérent, non transitif, et dont aucune puissance fn, n≠0, n'est isotope à l'identité. Cet exemple infirme une conjecture de [13]. L'exemple est obtenu en composant avec soin le temps t d'un flot d'Anosov non transitif bien choisi avec un twist de Dehn.

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 fn is not isotopic to the identity for all n≠0. This example contradicts a conjecture in [13]. The main idea is to consider a well-understood time-t map of a non-transitive Anosov flow and then carefully compose with a Dehn twist.

Publié le :
DOI : 10.24033/asens.2311
Classification : 37D30.
Keywords: Partially hyperbolic diffeomorphisms, classification.
Mot clés : Difféomorphismes partiellement hyperboliques, classification. 
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     title = {Anomalous partially  hyperbolic diffeomorphisms {I:}  dynamically coherent examples},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     pages = {1387--1402},
     publisher = {Soci\'et\'e Math\'ematique de France. Tous droits r\'eserv\'es},
     volume = {Ser. 4, 49},
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Bonatti, Christian; Parwani, Kamlesh; Potrie, Rafael. Anomalous partially  hyperbolic diffeomorphisms I:  dynamically coherent examples. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 49 (2016) no. 6, pp. 1387-1402. doi : 10.24033/asens.2311. http://www.numdam.org/articles/10.24033/asens.2311/

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