论文标题
平面分段线性矢量字段的Melnikov分析具有代数开关曲线$ y^n-x^m = 0 $
Melnikov analysis for planar piecewise linear vector fields with algebraic switching curve $y^n-x^m=0$
论文作者
论文摘要
本文致力于研究最大限制周期数，即$ h（m，n）$的平面分段线性差异系统，其两个区域由曲线$ y^n-x^m = 0 $隔开，$ n，m $是正整数。更确切地说，我们提供较低的估计值为$ h（m，n）$。对于所有$ m，n \ in \ mathbb {n} $，用于线性中心的分段线性扰动，使用有关Chebyshev系统的一些最新结果，具有积极的精度和Melnikov理论
This paper is devoted to the study of the maximum number of limit cycles, $H(m,n)$, of a planar piecewise linear differential system with two zones separated by the curve $y^n-x^m=0$, with $n,m$ being positive integers. More precisely, we provide a lower estimate of $ H(m,n)$. for all $m,n\in \mathbb{N}$, for piecewise linear perturbations of the linear center using some recent results about Chebyshev systems with positive accuracy and Melnikov Theory
