Rigidity of Lyapunov exponents for derived from Anosov diffeomorphisms
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866909307131396096 |
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| author | Costa, José Santana Tahzibi, Ali |
| author_facet | Costa, José Santana Tahzibi, Ali |
| contents | For a class of volume preserving partially hyperbolic diffeomorphisms (or non-uniformly Anosov) $f\colon {\T}^d\rightarrow{\T}^d$ homotopic to linear Anosov automorphism, we show that the sum of the positive (negative) Lyapunov exponents of $f$ is bounded above (resp. below) by the sum of the positive (resp. negative) Lyapunov exponents of its linearization. We show this for some classes of derived from Anosov (DA) and non-uniformly hyperbolic systems with dominated splitting, in particular for examples described by C. Bonatti and Viana. The results in this paper address a flexibility program by J. Bochi, A. Katok and F. Rodriguez Hertz. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_06657 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Rigidity of Lyapunov exponents for derived from Anosov diffeomorphisms Costa, José Santana Tahzibi, Ali Dynamical Systems For a class of volume preserving partially hyperbolic diffeomorphisms (or non-uniformly Anosov) $f\colon {\T}^d\rightarrow{\T}^d$ homotopic to linear Anosov automorphism, we show that the sum of the positive (negative) Lyapunov exponents of $f$ is bounded above (resp. below) by the sum of the positive (resp. negative) Lyapunov exponents of its linearization. We show this for some classes of derived from Anosov (DA) and non-uniformly hyperbolic systems with dominated splitting, in particular for examples described by C. Bonatti and Viana. The results in this paper address a flexibility program by J. Bochi, A. Katok and F. Rodriguez Hertz. |
| title | Rigidity of Lyapunov exponents for derived from Anosov diffeomorphisms |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2310.06657 |