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arXiv · 2304.06995

An Infinite-dimensional KAM Theorem with Normal Degeneracy

Jiayin Du·Lu Xu·Yong Li
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Abstract

In this paper, we consider a classical Hamiltonian normal form with degeneracy in normal direction. In previous results, one needs to assume that the perturbation satisfies certain non-degenerate conditions in order to remove the degeneracy in the normal form. In stead of that, we introduce a topological degree condition and a weak convexity condition, which are easy to be verified, and we prove the persistence of lower dimensional tori without any restriction on perturbation but only smallness and analyticity.

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Jiayin Du, Lu Xu, Yong Li. 2023-04-14. An Infinite-dimensional KAM Theorem with Normal Degeneracy. https://arxiv.org/abs/2304.06995

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