Golden mean renormalization for the almost Mathieu operator and related skew products
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2019
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866916290831056896 |
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| author | Koch, Hans |
| author_facet | Koch, Hans |
| contents | Considering SL(2,R) skew-product maps over circle rotations, we prove that a renormalization transformation associated with the golden mean alpha has a nontrivial periodic orbit of length 3. We also present some numerical results, including evidence this period 3 describes scaling properties of the Hofstadter butterfly near the top of the spectrum at alpha, and scaling properties of the generalized eigenfunction for this energy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1907_06804 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Golden mean renormalization for the almost Mathieu operator and related skew products Koch, Hans Mathematical Physics 37F25, 37E20, 47A10 Considering SL(2,R) skew-product maps over circle rotations, we prove that a renormalization transformation associated with the golden mean alpha has a nontrivial periodic orbit of length 3. We also present some numerical results, including evidence this period 3 describes scaling properties of the Hofstadter butterfly near the top of the spectrum at alpha, and scaling properties of the generalized eigenfunction for this energy. |
| title | Golden mean renormalization for the almost Mathieu operator and related skew products |
| topic | Mathematical Physics 37F25, 37E20, 47A10 |
| url | https://arxiv.org/abs/1907.06804 |