Transitive partially hyperbolic diffeomorphisms with one-dimensional neutral center

Authors :: Jinhua Zhang
Christian Bonatti
Institut de Mathématiques de Bourgogne [Dijon] (IMB)
Centre National de la Recherche Scientifique (CNRS)-Université de Franche-Comté (UFC)
Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université de Bourgogne (UB)
School of Mathematical Sciences [Beijing] (SMS)
Beijing Normal University (BNU)
European Research Council (ERC)692925Beihang University
Source :: Science China Mathematics, Science China Mathematics, Science China Press, 2020, 63 (9), pp.1647-1670. ⟨10.1007/s11425-019-1751-2⟩
Publication Year :: 2020
Publisher :: Springer Science and Business Media LLC, 2020.
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.<br />29 pages, 2 figures

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