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Transitive partially hyperbolic diffeomorphisms with one-dimensional neutral center

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Abstract

In this paper, we study transitive partially hyperbolic diffeomorphisms with one-dimensional topologically neutral center, meaning that the length of the iterate of small center segments remains small. Such systems are dynamically coherent. We show that there exists a continuous metric along the center foliation which is invariant under the dynamics. As an application, we classify the transitive partially hyperbolic diffeomorphisms on 3-manifolds with topologically neutral center.

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Acknowledgements

The second author was supported by the European Research Council (Grant No. 692925) and the starting grant from Beihang University. The second author thanks Institut de Mathématiques de Bourgogne and Laboratoire de Mathématiques d’Orsay for hospitality.

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Authors and Affiliations

  1. Institut de Mathématiques de Bourgogne, Université de Bourgogne, Dijon, 21104, France

    Christian Bonatti

  2. School of Mathematical Sciences, Beihang University, Beijing, 100191, China

    Jinhua Zhang

Authors
  1. Christian Bonatti
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  2. Jinhua Zhang
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Correspondence to Jinhua Zhang.

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To the Memory of Professor Shantao Liao

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Bonatti, C., Zhang, J. Transitive partially hyperbolic diffeomorphisms with one-dimensional neutral center. Sci. China Math. 63, 1647–1670 (2020). https://doi.org/10.1007/s11425-019-1751-2

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  • DOI: https://doi.org/10.1007/s11425-019-1751-2

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