2006/09/13 by F. Rodriguez Hertz, Federico Rodriguez Hertz, MA. Rodriguez Hertz +6
Mathematics · Physics and Astronomy · #37D30 (Primary) 37D10 (Secondary) #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #math.DS #msc:37D10 #msc:37D30
paper · pdf · doi:10.48550/arxiv.math/0609365
8 pages
arxiv created 2006/09/13 · openalex publication_date 2006/09/13 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove, for f a partially hyperbolic diffeomorphism with center dimension one, two results about the integrability of its central bundle. On one side, we show that if the non wandering set of f is the whole manifold, and the manifold is 3 dimensional, then the absence of periodic points implies the unique integrability of the central bundle. On the opposite side, we prove that any periodic point p of large period n has an f n invariant center manifold, everywhere tangent to the center bundle. We also obtain, as a consequence of the last result, that there is an open and dense subset of C 1 robustly transitive and partially hyperbolic diffeomorphisms with center dimension one, such that either the strong stable or the strong unstable foliation is minimal. This generalizes a result obtained in BDU for 3 dimensional manifolds to any dimension.