一类(4,3)型Liénard系统的阿贝尔积分零点个数  

The Number of Zeros for Abelian Integral of a Liénard System with (4,3) Type

作　　者：李成群[1] 郭慧[2] 韦敏志[1] 

机构地区：[1]广西财经学院,广西 南宁 [2]广西大学,广西 南宁

出　　处：《应用数学进展》2021年第7期2500-2510,共11页Advances in Applied Mathematics

摘　　要：Liénard系统在动力系统理论与应用方面是一个非常重要的非线性震荡器模型,大量的国内外学者对其进行了广泛而深刻的研究。当扰动项为零时,系统变为哈密顿系统。关于该系统的阿贝尔积分零点个数研究一直是近年来研究的热点,大量的研究人员都为此展开了激烈的讨论。本文着重考虑含有扰动项的Liénard系统的阿贝尔积分,根据阿贝尔积分生成元的切比雪夫理论,结合多项式符号计算技术证明阿贝尔积分零点个数的上界。The Liénard system is a very important nonlinear oscillator model in dynamic system theory and applications. A large number of domestic and foreign scholars have conducted extensive and in- depth research on it. When the puturbation is zero, the system becomes a Hamiltonian system. The study on the Abel integral zero number of this system has been a hot topic in recent years, there are lot of researchers have launched fierce discussions. This paper focuses on the Abel integral of the Liénard system with a perturbation term. According to the Chebyshev theory of the Abel integral generator and the progressive development formula of the Abel integral, combining with the polynomial symbol calculation technique to prove the upper bound of the number of zero points of the Abel integral.

关 键 词：LIÉNARD系统 阿贝尔积分 零点个数 切比雪夫理论 Sturm定理 

分 类 号：O17[理学—数学]