Topological structure of (partially) hyperbolic sets with positive volume
نویسندگان
چکیده
منابع مشابه
6 Topological Structure of ( Partially ) Hyperbolic Sets with Positive Volume
We consider both hyperbolic sets and partially hyperbolic sets attracting a set of points with positive volume in a Riemannian manifold. We obtain several results on the topological structure of such sets for diffeomorphisms whose differentiability is bigger than one. We show in particular that there are no partially hyperbolic horseshoes with positive volume for such diffeomorphisms. We also g...
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An attractor Λ for a 3-vector field X is singular-hyperbolic if all its singularities are hyperbolic and it is partially hyperbolic with volume expanding central direction. We prove that C singularhyperbolic attractors, for some α > 0, always have zero volume, thus extending an analogous result for uniformly hyperbolic attractors. The same result holds for a class of higher dimensional singular...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2008
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-08-04484-x