扰动片断线性哈密顿系统的两个猜想的证明

IF 1.8 3区数学 Q1 MATHEMATICS, APPLIED

Nonlinear Analysis-Real World Applications Pub Date : 2024-08-16 DOI:10.1016/j.nonrwa.2024.104195

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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

Nonlinear Analysis-Real World Applications 数学-应用数学

CiteScore

3.80

自引率

5.00%

发文量

176

审稿时长

59 days

期刊介绍： Nonlinear Analysis: Real World Applications welcomes all research articles of the highest quality with special emphasis on applying techniques of nonlinear analysis to model and to treat nonlinear phenomena with which nature confronts us. Coverage of applications includes any branch of science and technology such as solid and fluid mechanics, material science, mathematical biology and chemistry, control theory, and inverse problems. The aim of Nonlinear Analysis: Real World Applications is to publish articles which are predominantly devoted to employing methods and techniques from analysis, including partial differential equations, functional analysis, dynamical systems and evolution equations, calculus of variations, and bifurcations theory.