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arXiv · 2508.05147

Gevrey KAM equilibria for quasi-periodic long-range Frenkel-Kontorova models

Yujia An·Xifeng Su
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Abstract

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.

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Yujia An, Xifeng Su. 2025-08-07. Gevrey KAM equilibria for quasi-periodic long-range Frenkel-Kontorova models. https://arxiv.org/abs/2508.05147

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