Monochromatic nonuniform hyperbolicity
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914032774021120 |
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| author | Bochi, Jairo |
| author_facet | Bochi, Jairo |
| contents | We construct examples of continuous $\mathrm{GL}(2,\mathbb{R})$-cocycles which are not uniformly hyperbolic despite having the same non-zero Lyapunov exponents with respect to all invariant measures. The base dynamics can be any non-trivial subshift of finite type. According to a theorem of DeWitt--Gogolev and Guysinsky, such cocycles cannot be Hölder-continuous. Our construction uses the nonuniformly hyperbolic cocycles discovered by Walters in 1984. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_03878 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Monochromatic nonuniform hyperbolicity Bochi, Jairo Dynamical Systems 37D25 We construct examples of continuous $\mathrm{GL}(2,\mathbb{R})$-cocycles which are not uniformly hyperbolic despite having the same non-zero Lyapunov exponents with respect to all invariant measures. The base dynamics can be any non-trivial subshift of finite type. According to a theorem of DeWitt--Gogolev and Guysinsky, such cocycles cannot be Hölder-continuous. Our construction uses the nonuniformly hyperbolic cocycles discovered by Walters in 1984. |
| title | Monochromatic nonuniform hyperbolicity |
| topic | Dynamical Systems 37D25 |
| url | https://arxiv.org/abs/2408.03878 |