关于共振重叠发生的一点注记

IF 0.8 4区数学 Q3 MATHEMATICS, APPLIED

Regular and Chaotic Dynamics Pub Date : 2023-10-20 DOI:10.1134/S1560354723040056

Jacques Fejoz, Marcel Guardia

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引用次数: 0

摘要

Chirikov著名的共振重叠准则在天体力学和哈密顿动力学中被广泛用于检测全局不稳定性，但很少是严格的。我们介绍了两个简单的哈密顿系统，每个系统都取决于两个参数，分别测量到共振重叠的距离和不可积分性。在参数平面的某个薄区域内，经典微扰理论证明了全局不稳定性和符号动力学的存在，从而说明了Chirikov准则。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

A Remark on the Onset of Resonance Overlap

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A Remark on the Onset of Resonance Overlap

Chirikov’s celebrated criterion of resonance overlap has been widely used in celestial mechanics and Hamiltonian dynamics to detect global instability, but is rarely rigorous. We introduce two simple Hamiltonian systems, each depending on two parameters measuring, respectively, the distance to resonance overlap and nonintegrability. Within some thin region of the parameter plane, classical perturbation theory shows the existence of global instability and symbolic dynamics, thus illustrating Chirikov’s criterion.

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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.