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Transitive partially hyperbolic diffeomorphisms with one-dimensional neutral center
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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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Partially hyperbolic diffeomorphisms homotopic to the identity in dimension 3, Part I: The dynamically coherent case
On hyperbolic and Seifert fibered 3-manifolds, dynamically coherent partially hyperbolic diffeomorphisms homotopic to the identity are, up to iterate, leaf conjugate to time-one maps of topological Anosov flows.
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