Gevrey KAM equilibria for quasi-periodic long-range Frenkel-Kontorova models
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866913978870923264 |
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| author | An, Yujia Su, Xifeng |
| author_facet | An, Yujia Su, Xifeng |
| contents | We consider models of one-dimensional chains of non-nearest neighbor and many-body interacting particles subjected to quasi-periodic media. We extend the results in \cite{12Su&delaLlavelongrange} from analytic to Gevrey regularity potentials. More precisely, we establish an a posteriori KAM theorem showing that in the Gevrey topology, given an approximate solution of equilibrium equation, which satisfies some appropriate non-degeneracy conditions and decay property, then there is a true solution nearby and the solution preserves both the quasi-periodicity and Gevrey regularity. The method of proof is based on a combination of quasi-Newton methods and delicate estimates in spaces of Gevrey functions. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_05147 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Gevrey KAM equilibria for quasi-periodic long-range Frenkel-Kontorova models An, Yujia Su, Xifeng Dynamical Systems 37J40, 70K43 We consider models of one-dimensional chains of non-nearest neighbor and many-body interacting particles subjected to quasi-periodic media. We extend the results in \cite{12Su&delaLlavelongrange} from analytic to Gevrey regularity potentials. More precisely, we establish an a posteriori KAM theorem showing that in the Gevrey topology, given an approximate solution of equilibrium equation, which satisfies some appropriate non-degeneracy conditions and decay property, then there is a true solution nearby and the solution preserves both the quasi-periodicity and Gevrey regularity. The method of proof is based on a combination of quasi-Newton methods and delicate estimates in spaces of Gevrey functions. |
| title | Gevrey KAM equilibria for quasi-periodic long-range Frenkel-Kontorova models |
| topic | Dynamical Systems 37J40, 70K43 |
| url | https://arxiv.org/abs/2508.05147 |