Mathematics – Dynamical Systems
Scientific paper
2006-03-06
Mathematics
Dynamical Systems
21 pages
Scientific paper
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 give a description of the limit set of almost every point belonging to a hyperbolic set or a partially hyperbolic set with positive volume.
Alves Jose F.
Pinheiro Vilton
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