Simple Lyapunov spectrum of partially hyperbolic diffeomorphisms
Abstract
Abstract We study the simplicity of the Lyapunov spectrum of partially hyperbolic diffeomorphisms. We prove that simplicity of the Lyapunov spectrum holds in a $C^{r}$-dense and $C^{2}$-open subset of a certain class of volume-preserving partially hyperbolic diffeomorphisms. Also we demonstrate that a class of partially hyperbolic maps has simple spectrum generically for the measures of maximal entropy. In order to establish these results, we give a criterion for simplicity of the Lyapunov spectrum in terms of periodic points homoclinically related to the invariant measure.
Fields of Study & Subjects
Mathematical Dynamics and Fractals
Quantum chaos and dynamical systems
Advanced Differential Equations and Dynamical Systems
Publication details
- Journal / source
- International Mathematics Research Notices
- Volume
- 2026
- Issue
- 18
- Publication date
- 1 September 2026
- Language
- EN