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CENTER MANIFOLDS FOR PARTIALLY HYPERBOLIC SETS WITHOUT STRONG UNSTABLE CONNECTIONS

Part of: Smooth dynamical systems: general theory Dynamical systems with hyperbolic behavior

Published online by Cambridge University Press:  11 March 2015

Christian Bonatti  and
Sylvain Crovisier
Christian Bonatti
Affiliation:
Institut de Mathématiques de Bourgogne, CNRS - URM 5584, Université de Bourgogne, Dijon 21004, France (bonatti@u-bourgogne.fr)
Sylvain Crovisier
Affiliation:
Laboratoire de Mathématiques d’Orsay, CNRS - UMR 8628, Université Paris-Sud 11, Orsay 91405, France (Sylvain.Crovisier@math.u-psud.fr)
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Abstract

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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.

Keywords

center manifoldpartial hyperbolicityheteroclinic intersection

MSC classification

Primary: 37D10: Invariant manifold theory
Secondary: 37D30: Partially hyperbolic systems and dominated splittings 37C29: Homoclinic and heteroclinic orbits
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 15 , Issue 4 , October 2016 , pp. 785 - 828
Copyright
© Cambridge University Press 2015 

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