Persistence of Degenerate Lower Dimensional Invariant Tori with Prescribed Frequencies in Reversible Systems

被引：1

作者：

Yang, Xiaomei ^{[1
]}

Xu, Junxiang ^{[1
]}

Jiang, Shunjun ^{[2
]}

机构：

[1] Southeast Univ, Sch Math, Nanjing 210096, Peoples R China

[2] Nanjing Tech Univ, Coll Sci, Nanjing 210009, Peoples R China

来源：

JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS | 2023年 / 35卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Reversible system; KAM iteration; Invariant tori; Degenerate equilibrium; RESONANT SURFACES; PERTURBATIONS; THEOREM;

D O I：

10.1007/s10884-021-09989-x

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper considers small perturbations of an integrable reversible system which has a degenerated lower dimensional invariant torus in some sense. In the presence of some higher-order terms, by some KAM technique and the stability of critical points of real analytic functions developed for hamiltonian systems, we prove the persistence of the degenerate lower dimensional invariant torus with prescribed frequencies without extra conditions on the perturbations besides the smallness. This result is an extension of the partial result of hamiltonian systems in Xu and You (Regul Chaotic Dyn 25(6):616-650, 2020) to reversible systems.

引用

页码：329 / 354

页数：26

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