English

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 CrC^r-accumulated by C2C^2-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}
}