Simple Lyapunov spectrum of partially hyperbolic diffeomorphisms
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915395213983744 |
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| author | Marin, Karina Obata, Davi Poletti, Mauricio |
| author_facet | Marin, Karina Obata, Davi Poletti, Mauricio |
| contents | We study the simplicity of the Lyapunov spectrum of partially hyperbolic diffeomorphisms. We prove that a class of volume-preserving partially hyperbolic diffeomorphisms is $C^r$-accumulated by $C^2$-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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_12715 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Simple Lyapunov spectrum of partially hyperbolic diffeomorphisms Marin, Karina Obata, Davi Poletti, Mauricio Dynamical Systems 37D30, 37D25 We study the simplicity of the Lyapunov spectrum of partially hyperbolic diffeomorphisms. We prove that a class of volume-preserving partially hyperbolic diffeomorphisms is $C^r$-accumulated by $C^2$-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. |
| title | Simple Lyapunov spectrum of partially hyperbolic diffeomorphisms |
| topic | Dynamical Systems 37D30, 37D25 |
| url | https://arxiv.org/abs/2507.12715 |