Partially Hyperbolic Sets with a Dynamically Minimal Invariant Lamination

Abstract

We study partially hyperbolic sets of C1-diffeomorphisms. For these sets there are defined the strong stable and strong unstable laminations. A lamination is called dynamically minimal when the orbit of each leaf intersects the set densely. We prove that partially hyperbolic sets having a dynamically minimal lamination have empty interior. We also study the Lebesgue measure and the spectral decomposition of these sets. These results can be ap- plied to C1-generic/robustly transitive attractors with one-dimensional center bundle.