具有非单调旋转的二维哈密顿系统的准周期参数扰动

IF 0.8 4区数学 Q3 MATHEMATICS, APPLIED Regular and Chaotic Dynamics Pub Date : 2024-03-11 DOI:10.1134/S1560354724010052

Kirill E. Morozov, Albert D. Morozov

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引用次数: 0

摘要

我们研究了具有非单调旋转的二维哈密顿系统的非保守准周期（频率）扰动。假设扰动包含所谓的参数项。描述了退化共振附近解的行为。找到了共振（(m+1)\）维不变环存在的条件，而未扰动系统中不存在这些不变环。指出了可能存在这种转矩的扰动类别。结果被应用于参数准周期扰动下的非对称达芬方程。

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Quasi-Periodic Parametric Perturbations of Two-Dimensional Hamiltonian Systems with Nonmonotonic Rotation

We study nonconservative quasi-periodic (with \(m\) frequencies) perturbations of two-dimensional Hamiltonian systems with nonmonotonic rotation. It is assumed that the perturbation contains the so-called parametric terms. The behavior of solutions in the vicinity of degenerate resonances is described. Conditions for the existence of resonance \((m+1)\)-dimensional invariant tori for which there are no generating ones in the unperturbed system are found. The class of perturbations for which such tori can exist is indicated. The results are applied to the asymmetric Duffing equation under a parametric quasi-periodic perturbation.

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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.