CENTER MANIFOLDS FOR PARTIALLY HYPERBOLIC SETS WITHOUT STRONG UNSTABLE CONNECTIONS

CENTER MANIFOLDS FOR PARTIALLY HYPERBOLIC SETS WITHOUT STRONG UNSTABLE CONNECTIONS

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 poi...

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Veröffentlicht in:Journal of the Institute of Mathematics of Jussieu 2016-10, Vol.15 (4), p.785-828
Hauptverfasser: Bonatti, Christian, Crovisier, Sylvain
Format: Artikel
Sprache:eng
Schlagworte:
Dynamics
Invariants
Joints
Manifolds
Mathematical analysis
Mathematics
Theoretical mathematics
Topological manifolds
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Beschreibung
Zusammenfassung: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.
ISSN:1474-7480
1475-3030
DOI:10.1017/S1474748015000055