Quantitative Reducibility of $C^k$ Quasi-Periodic Cocycles
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866917681586765824 |
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| author | Cai, Ao Lv, Huihui Wang, Zhiguo |
| author_facet | Cai, Ao Lv, Huihui Wang, Zhiguo |
| contents | This paper establishes an extreme $C^k$ reducibility theorem of quasi-periodic $SL(2, \mathbb{R})$ cocycles in the local perturbative region, revealing both the essence of Eliasson [Commun.Math.Phys.1992] and Hou-You [Invent.Math.2012] in respectively the non-resonant and resonant cases. By paralleling further the reducibility process with the almost reducibility, we are able to acquire the least initial regularity as well as the least loss of regularity for the whole KAM iterations. This, in return, makes various spectral applications of quasi-periodic Schrödinger operators wide open. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_09132 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quantitative Reducibility of $C^k$ Quasi-Periodic Cocycles Cai, Ao Lv, Huihui Wang, Zhiguo Dynamical Systems Mathematical Physics This paper establishes an extreme $C^k$ reducibility theorem of quasi-periodic $SL(2, \mathbb{R})$ cocycles in the local perturbative region, revealing both the essence of Eliasson [Commun.Math.Phys.1992] and Hou-You [Invent.Math.2012] in respectively the non-resonant and resonant cases. By paralleling further the reducibility process with the almost reducibility, we are able to acquire the least initial regularity as well as the least loss of regularity for the whole KAM iterations. This, in return, makes various spectral applications of quasi-periodic Schrödinger operators wide open. |
| title | Quantitative Reducibility of $C^k$ Quasi-Periodic Cocycles |
| topic | Dynamical Systems Mathematical Physics |
| url | https://arxiv.org/abs/2403.09132 |