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CENTER MANIFOLDS FOR PARTIALLY HYPERBOLIC SETS WITHOUT STRONG UNSTABLE CONNECTIONS

  • Christian Bonatti (a1) and Sylvain Crovisier (a2)

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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References

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