Linear Estimation of the Number of Zeros of Abelian Integrals for Some Cubic Isochronous Centers
Linear Estimation of the Number of Zeros of Abelian Integrals for Some Cubic Isochronous Centers
复制标题
DOI：
10.1006/jdeq.2001.4064
复制
发表时间：
2002-04
影响因子：
2.4
通讯作者：
Chengzhi Li;Weigu Li;J. Llibre;Zhifen Zhang
中科院分区：
文献类型：
--
作者：
Chengzhi Li;Weigu Li;J. Llibre;Zhifen Zhang
摘要 本文由两部分组成。在第一部分中，我们研究多项式系统的圆锥中心（中心类型奇点附近的所有轨道都是圆锥曲线）与等时中心之间的关系。在第二部分中，我们研究当我们在所有 n 次多项式系统中扰动此类系统时，从所有轨道均由二次曲线形成的立方可逆等时中心的周期轨道分叉的极限环的数量。
Abstract This paper consists of two parts. In the first part we study the relationship between conic centers (all orbits near a singular point of center type are conics) and isochronous centers of polynomial systems. In the second part we study the number of limit cycles that bifurcate from the periodic orbits of cubic reversible isochronous centers having all their orbits formed by conics, when we perturb such systems inside the class of all polynomial systems of degree n .