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Some results on the integrability of the center bundle for partially hyperbolic diffeomorphisms

F. Rodriguez Hertz·MA. Rodriguez Hertz·R. Ures
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Abstract

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.

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F. Rodriguez Hertz, MA. Rodriguez Hertz, R. Ures. 2006-09-13. Some results on the integrability of the center bundle for partially hyperbolic diffeomorphisms. https://arxiv.org/abs/math/0609365

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