Simple Lyapunov spectrum of partially hyperbolic diffeomorphisms
Dynamical Systems
2025-07-18 v1
Abstract
We study the simplicity of the Lyapunov spectrum of partially hyperbolic diffeomorphisms. We prove that a class of volume-preserving partially hyperbolic diffeomorphisms is -accumulated by -open sets with simple spectrum. Also we prove that a class of partially hyperbolic maps has simple spectrum generically for the measures of maximal entropy. In order to prove these results, we give a criterion for simplicity of the Lyapunov spectrum in terms of periodic points homoclinically related to the invariant measure.
Keywords
Cite
@article{arxiv.2507.12715,
title = {Simple Lyapunov spectrum of partially hyperbolic diffeomorphisms},
author = {Karina Marin and Davi Obata and Mauricio Poletti},
journal= {arXiv preprint arXiv:2507.12715},
year = {2025}
}