Transitive partially hyperbolic diffeomorphisms with one-dimensional neutral center

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.

arXiv comment29 pages, 2 figures

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Cited by in corpus (1)

• Classification of Conditional Measures Along Certain Invariant One-Dimensional Foliations