Center Manifolds for Partially Hyperbolic Sets 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 : lundi 9 octobre 2017 - 11:32:27

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Christian Bonatti, Sylvain Crovisier. Center Manifolds for Partially Hyperbolic Sets Without Strong Unstable Connections. Journal of the Institute of Mathematics of Jussieu, Cambridge University Press (CUP), 2016, 15 (04), pp.785 - 828. 〈https://www.cambridge.org/core/journals/journal-of-the-institute-of-mathematics-of-jussieu/article/div-classtitlecenter-manifolds-for-partially-hyperbolic-sets-without-strong-unstable-connectionsdiv/E95A4E35918A12752403AF746798BC94〉. 〈10.1017/S1474748015000055〉. 〈hal-01414891〉

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