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| Main Authors: | , , |
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| Format: | Preprint |
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2020
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2006.03381 |
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| _version_ | 1866910794842636288 |
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| author | Xu, Jiahao Ge, Lingrui Wang, Yiqian |
| author_facet | Xu, Jiahao Ge, Lingrui Wang, Yiqian |
| contents | In this paper, we study the regularity of the Lyapunov exponent for quasiperiodic Schrödinger cocycles with $C^2$ cos-type potentials, large coupling constants, and a fixed Diophantine frequency. We obtain the absolute continuity of the Lyapunov exponent. Moreover, we prove the Lyapunov exponent is $\frac{1}{2}$-Hölder continuous. Furthermore, for any given $r\in (\frac12, 1)$, we can find some energy in the spectrum where the local regularity of the Lyapunov exponent is between $(r-ε)$-Hölder continuity and $(r+ε)$-Hölder continuity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2006_03381 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | The precise regularity of the Lyapunov exponent for $C^2$ Cos-type quasiperiodic Schrödinger cocycles with large couplings Xu, Jiahao Ge, Lingrui Wang, Yiqian Dynamical Systems 37D25 In this paper, we study the regularity of the Lyapunov exponent for quasiperiodic Schrödinger cocycles with $C^2$ cos-type potentials, large coupling constants, and a fixed Diophantine frequency. We obtain the absolute continuity of the Lyapunov exponent. Moreover, we prove the Lyapunov exponent is $\frac{1}{2}$-Hölder continuous. Furthermore, for any given $r\in (\frac12, 1)$, we can find some energy in the spectrum where the local regularity of the Lyapunov exponent is between $(r-ε)$-Hölder continuity and $(r+ε)$-Hölder continuity. |
| title | The precise regularity of the Lyapunov exponent for $C^2$ Cos-type quasiperiodic Schrödinger cocycles with large couplings |
| topic | Dynamical Systems 37D25 |
| url | https://arxiv.org/abs/2006.03381 |