English

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.

Keywords

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}
}
R2 v1 2026-06-22T18:53:07.089Z