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arXiv · 1904.05295

Transitive partially hyperbolic diffeomorphisms with one-dimensional neutral center

Christian Bonatti·Jinhua Zhang
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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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Christian Bonatti, Jinhua Zhang. 2019-04-10. Transitive partially hyperbolic diffeomorphisms with one-dimensional neutral center. https://doi.org/10.1007/s11425-019-1751-2

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