标题： 从权次数为2的拟齐次多项式中心分支出的非光滑扰动极限环 显示英文标题

标题： Limit cycles bifurcating from the quasi-homogeneous polynomial centers of weight-degree 2 under non-smooth perturbations

摘要： 我们研究了当一族三次多项式微分中心在所有三次分段光滑多项式类中受到扰动时，从周期环域分支出的最大极限环数目。考虑的族是唯一的权齐次权次数为2的多项式微分系统族，并且具有中心。当切换线为$x=0$或$y=0$时，我们利用一阶平均法得到了受扰系统极限环数目的精确界。我们的结果表明，非光滑系统可以比光滑系统具有更多的极限环，并且切换线在非光滑系统的动力学中起着重要作用。 显示英文摘要

摘要： We investigate the maximum number of limit cycles bifurcating from the period annulus of a family of cubic polynomial differential centers when it is perturbed inside the class of all cubic piecewise smooth polynomials. The family considered is the unique family of weight-homogeneous polynomial differential systems of weight-degree 2 with a center. When the switching line is $x=0$ or $y=0$, we obtain the sharp bounds of the number of limit cycles for the perturbed systems by using the first order averaging method. Our results indicate that non-smooth systems can have more limit cycles than smooth ones, and the switching lines play an important role in the dynamics of non-smooth systems.