It is known that under Kolmogorov’s nondegeneracy condition, the nondegenerate hyperbolic invariant torus with Diophantine frequencies will persist under small perturbations, meaning that the perturbed system still has an invariant torus with prescribed frequencies. However, the degenerate torus is sensitive to perturbations. In this paper, we prove the persistence of two classes of hyperbolic-type degenerate lower-dimensional invariant tori, one of them corrects an earlier work [34] by the second author. The proof is based on a modified KAM iteration and analysis of stability of degenerate critical points of analytic functions.

中文翻译：

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哈密​​顿系统中具有规定频率的双曲型简并低维不变托里的持久性

众所周知，在Kolmogorov的非简并性条件下，具有丢丢丁频率的非简并双曲不变环将在小扰动下持续存在，这意味着被扰动的系统仍然具有规定频率的不变环。但是，退化的圆环对扰动敏感。在本文中，我们证明了两类双曲型简并的低维不变花托的持久性，其中之一纠正了第二作者的早期工作[34]。该证明是基于改进的KAM迭代和分析函数的退化临界点稳定性的分析。