对某些三维等时中心Abel积分零点个数的线形估计

北京大学学报（自然科学版）

对某些三维等时中心Abel积分零点个数的线形估计

梁爽

北京大学数学科学学院，北京，100871

收稿日期:2003-09-08 出版日期:2005-01-20 发布日期:2005-01-20

Linear Estimation of the Number of Zeros of Abelian Integrals for Cubic Isochronous Centers

LIANG Shuang

School of Mathematical Sciences, Peking University, Beijing, 100871

Received:2003-09-08 Online:2005-01-20 Published:2005-01-20

摘要/Abstract

摘要： 研究所有轨道都是由圆锥曲线组成的三维等时中心的周期轨道。当系统是 n 次多项式系统时，经过扰动，考察它分岔出来的极限环的个数。

关键词: 极限环, 微分系, Abel积分

Abstract: It is studied that the number of limit cycles that bifurcate from the periodic orbit of cubic isorhronous centers, formed by conics, when perturbing such systems inside the class of all polynomial systems of degree n.

Key words: limit cycles, differential systems, Abelian integrals

中图分类号:

O156.4

梁爽. 对某些三维等时中心Abel积分零点个数的线形估计[J]. 北京大学学报（自然科学版）.

LIANG Shuang. Linear Estimation of the Number of Zeros of Abelian Integrals for Cubic Isochronous Centers[J]. Acta Scientiarum Naturalium Universitatis Pekinensis.