论圆柱上近哈密尔顿系统极限循环的双同向分岔

IF 1.9 3区数学 Q1 MATHEMATICS

Qualitative Theory of Dynamical Systems Pub Date : 2024-07-30 DOI:10.1007/s12346-024-01107-8

Ai Ke, Junmin Yang

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引用次数: 0

摘要

我们研究了近哈密尔顿系统在圆柱体上的双同向环附近的极限循环分岔问题。我们得到了一个充分条件，即通过双同向环附近三个周期轨道族对应的三个梅利尼科夫函数的展开系数，找到环附近极限循环的最大数量下限。我们还将主要结果应用于一类圆柱系统。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

On Double Homoclinic Bifurcation of Limit Cycles in Near-Hamiltonian Systems on the Cylinder

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On Double Homoclinic Bifurcation of Limit Cycles in Near-Hamiltonian Systems on the Cylinder

We study the bifurcation problem of limit cycles in near-Hamiltonian systems near a double homoclinic loop on the cylinder. We obtain a sufficient condition to find a lower bound of the maximal number of limit cycles near the loop by the coefficients of the expansions of the three Melnikov functions corresponding to the three families of periodic orbits near the double homoclinic loop. We also provide an application of our main results to a class of cylindrical systems.

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来源期刊

Qualitative Theory of Dynamical Systems MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.50

自引率

14.30%

发文量

130

期刊介绍： Qualitative Theory of Dynamical Systems (QTDS) publishes high-quality peer-reviewed research articles on the theory and applications of discrete and continuous dynamical systems. The journal addresses mathematicians as well as engineers, physicists, and other scientists who use dynamical systems as valuable research tools. The journal is not interested in numerical results, except if these illustrate theoretical results previously proved.