Log Hölder continuity of the rotation number
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910657980399616 |
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| author | Gorodetski, Anton Kleptsyn, Victor |
| author_facet | Gorodetski, Anton Kleptsyn, Victor |
| contents | We consider one-parameter families of smooth circle cocycles over an ergodic transformation in the base, and show that their rotation numbers must be log-Hölder regular with respect to the parameter. As an immediate application, we get a dynamical proof of 1D version of the Craig-Simon theorem that establishes that the integrated density of states of an ergodic Schrödinger operator must be log-Hölder. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_15462 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Log Hölder continuity of the rotation number Gorodetski, Anton Kleptsyn, Victor Dynamical Systems Spectral Theory 37E45, 37E10, 81Q10 We consider one-parameter families of smooth circle cocycles over an ergodic transformation in the base, and show that their rotation numbers must be log-Hölder regular with respect to the parameter. As an immediate application, we get a dynamical proof of 1D version of the Craig-Simon theorem that establishes that the integrated density of states of an ergodic Schrödinger operator must be log-Hölder. |
| title | Log Hölder continuity of the rotation number |
| topic | Dynamical Systems Spectral Theory 37E45, 37E10, 81Q10 |
| url | https://arxiv.org/abs/2410.15462 |