Partially Hyperbolic Sets with a Dynamically Minimal Invariant Lamination
Dynamical Systems
2017-03-23 v1
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.
Cite
@article{arxiv.1703.07413,
title = {Partially Hyperbolic Sets with a Dynamically Minimal Invariant Lamination},
author = {Felipe Nobili},
journal= {arXiv preprint arXiv:1703.07413},
year = {2017}
}