# Center manifolds for partially hyperbolic set without strong unstable connections

Abstract : We consider compact sets which are invariant and partially hyperbolic under the dynamics of a diffeomorphism of a manifold. We prove that such a set $K$ is contained in a locally invariant center submanifold if and only if each strong stable and strong unstable leaf intersects $K$ at exactly one point.
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https://hal-univ-bourgogne.archives-ouvertes.fr/hal-01414891
Contributeur : Imb - Université de Bourgogne <>
Soumis le : lundi 12 décembre 2016 - 16:26:30
Dernière modification le : vendredi 8 juin 2018 - 14:50:07

### Citation

Christian Bonatti, Sylvain Crovisier. Center manifolds for partially hyperbolic set without strong unstable connections. Journal of the Institute of Mathematics of Jussieu, Cambridge University Press (CUP), 2016, 15 (04), pp.785 - 828. ⟨10.1017/S1474748015000055⟩. ⟨hal-01414891⟩

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