Discontinuity of Lyapunov exponents for SL$(2,\mathbb{R})$ valued cocycles
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866911412026081280 |
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| author | Mamani, Edhin Saraiva, Raquel |
| author_facet | Mamani, Edhin Saraiva, Raquel |
| contents | We exhibit an example of discontinuity point for the Lyapunov exponents as a function of the cocycle in the $α$-Hölder topology. The linear cocycle taking values in $SL(2, \mathbb{R})$ is locally constant and defined over a Bernoulli shift. Our example extends Bocker-Viana's and Butler's results. In particular, it gives a partial answer to a question raised by Clark Butler. Finally, we give an example of discontinuity in the setting of $SL(m,\mathbb{R})$-valued cocycles, which is constructed from $SL(2, \mathbb{R})$-valued cocycles. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_20310 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Discontinuity of Lyapunov exponents for SL$(2,\mathbb{R})$ valued cocycles Mamani, Edhin Saraiva, Raquel Dynamical Systems We exhibit an example of discontinuity point for the Lyapunov exponents as a function of the cocycle in the $α$-Hölder topology. The linear cocycle taking values in $SL(2, \mathbb{R})$ is locally constant and defined over a Bernoulli shift. Our example extends Bocker-Viana's and Butler's results. In particular, it gives a partial answer to a question raised by Clark Butler. Finally, we give an example of discontinuity in the setting of $SL(m,\mathbb{R})$-valued cocycles, which is constructed from $SL(2, \mathbb{R})$-valued cocycles. |
| title | Discontinuity of Lyapunov exponents for SL$(2,\mathbb{R})$ valued cocycles |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2407.20310 |