Piecewise Smooth Perturbations to a Class of Planar Cubic Centers

Linping Peng, Yue Li, Dandi Sun
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Abstract

This paper studies the limit cycle bifurcations of a class of planar cubic isochronous centers. For different values of two key parameters, we give an estimate of the maximum number of limit cycles bifurcating from the period annulus of the unperturbed systems under arbitrarily small piecewise smooth polynomial perturbation. The main method and technique are based on the first order averaging theory for discontinuous systems and the Argument Principle in complex analysis.
一类平面三次中心的分段光滑摄动
研究了一类平面三次等时中心的极限环分岔问题。对于两个关键参数的不同取值,给出了任意小分段光滑多项式摄动下无摄动系统从周期环分叉的最大极限环数的估计。主要的方法和技术是基于不连续系统的一阶平均理论和复数分析中的参数原理。
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