论小参数哈密顿系统中具有规定频率的椭圆形低维不变矩阵

IF 0.8 4区数学 Q3 MATHEMATICS, APPLIED

Regular and Chaotic Dynamics Pub Date : 2024-08-04 DOI:10.1134/S156035472404004X

Hanru Zou, Junxiang Xu

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引用次数: 0

摘要

在本文中，我们考虑了在具有小参数的哈密顿系统中具有规定频率的椭圆低维不变环的持久性问题。在 Brjuno nondegeneracy 条件下，如果规定频率满足 Diophantine 条件，我们通过 KAM 技术证明，对于大多数 Lebesgue 度量意义上的小参数，哈密顿系统中存在一个低维不变环，其频率向量是规定频率的扩张。

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On Elliptic Lower-Dimensional Invariant Tori with Prescribed Frequencies in Hamiltonian Systems with Small Parameters

In this paper we consider the persistence of elliptic lower-dimensional invariant tori with prescribed frequencies in Hamiltonian systems with small parameters. Under the Brjuno nondegeneracy condition, if the prescribed frequencies satisfy a Diophantine condition, by the KAM technique we prove that for most of small parameters in the sense of Lebesgue measure, the Hamiltonian systems admit a lower-dimensional invariant torus whose frequency vector is a dilation of the prescribed frequencies.

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来源期刊

Regular and Chaotic Dynamics 物理-力学

CiteScore

2.50

自引率

7.10%

发文量

审稿时长

>12 weeks

期刊介绍： Regular and Chaotic Dynamics (RCD) is an international journal publishing original research papers in dynamical systems theory and its applications. Rooted in the Moscow school of mathematics and mechanics, the journal successfully combines classical problems, modern mathematical techniques and breakthroughs in the field. Regular and Chaotic Dynamics welcomes papers that establish original results, characterized by rigorous mathematical settings and proofs, and that also address practical problems. In addition to research papers, the journal publishes review articles, historical and polemical essays, and translations of works by influential scientists of past centuries, previously unavailable in English. Along with regular issues, RCD also publishes special issues devoted to particular topics and events in the world of dynamical systems.