Dynamics of Slow-Fast Hamiltonian Systems: The Saddle–Focus Case

IF 0.8 4区数学 Q3 MATHEMATICS, APPLIED

Regular and Chaotic Dynamics Pub Date : 2024-12-27 DOI:10.1134/S1560354724590039

Sergey V. Bolotin

引用次数: 0

Abstract

We study the dynamics of a multidimensional slow-fast Hamiltonian system in a neighborhood of the slow manifold under the assumption that the frozen system has a hyperbolic equilibrium with complex simple leading eigenvalues and there exists a transverse homoclinic orbit. We obtain formulas for the corresponding Shilnikov separatrix map and prove the existence of trajectories in a neighborhood of the homoclinic set with a prescribed evolution of the slow variables. An application to the \(3\) body problem is given.

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慢-快哈密顿系统动力学：鞍-焦点情况

本文研究了在慢流形的邻域中一个多维慢-快哈密顿系统的动力学问题，假设冻结系统具有一个双曲平衡，具有复简单的前导特征值，并且存在一个横向同斜轨道。我们得到了相应的Shilnikov分离矩阵映射的公式，并证明了具有给定慢变量演化的同斜集邻域中轨迹的存在性。给出了\(3\)体问题的一个应用。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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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.