# American Institute of Mathematical Sciences

June  2018, 38(6): 2717-2729. doi: 10.3934/dcds.2018114

## Partially hyperbolic sets with a dynamically minimal lamination

 Departamento de Matemática - Instituto Tecnológico de Aeronáutica (ITA) - Praça Marechal Eduardo Gomes, 50 - Vila das Acacias, São José dos Campos, CEP 12228-900, SP, Brazil

Received  March 2017 Revised  December 2017 Published  April 2018

We study partially hyperbolic sets of $C^1$-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 applied to $C^1$-generic/robustly transitive attractors with one-dimensional center bundle.

Citation: Luiz Felipe Nobili França. Partially hyperbolic sets with a dynamically minimal lamination. Discrete & Continuous Dynamical Systems - A, 2018, 38 (6) : 2717-2729. doi: 10.3934/dcds.2018114
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