扰动片断线性哈密顿系统的两个猜想的证明

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY Accounts of Chemical Research Pub Date : 2024-08-16 DOI:10.1016/j.nonrwa.2024.104195

Shiyou Sui , Yongkang Zhang , Baoyi Li

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引用次数: 0

摘要

本文研究了在片断平滑多项式的扰动下，从具有同室环或异室环的片断线性哈密顿系统中心分岔的极限循环数。通过研究一阶梅利尼科夫函数的生成函数的切比雪夫性质，我们得到了从周期环上分岔的极限周期数的尖锐边界，这证实了梁、韩和罗曼诺夫斯基（2012）以及梁和韩（2016）提出的猜想。

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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Proof of two conjectures for perturbed piecewise linear Hamiltonian systems

In this paper, we study the number of limit cycles bifurcating from the centers of piecewise linear Hamiltonian systems having either a homoclinic loop or a heteroclinic loop under the perturbations of piecewise smooth polynomials. By investigating the Chebyshev properties of generating functions of the first order Melnikov functions, we obtain the sharp bounds of the number of limit cycles bifurcating from the periodic annuluses, which confirm the conjectures proposed by Liang, Han and Romanovski (2012) and Liang and Han (2016).

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.

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