• 论文 •

### 一个二次可积系统在二次保守扰动下的分支

1. 北京航空航天大学 理学院
• 收稿日期:1998-10-14 出版日期:2000-02-29 发布日期:2010-09-27
• 作者简介:彭临平(1966-),女,山西临汾人,讲师,100083,北京.

PENG Lin-ping

1. Beijing University of Aeronautics and Astronautics,School of Science
• Received:1998-10-14 Online:2000-02-29 Published:2010-09-27

Abstract: The question on bifurcation of limit cycles in quadratic conservative perturbations of a quadratic integrable system is discussed. As a result of conservative perturbations, the first order Melnikov function for a perturbed system is identically equal to zero, so the second order Melnikov function has to be considered. The perturbation parameters which make no use in the first order Melnikov function may be important in the second order Melnikov function. Hence perturbed systems are more complicated. With the help of the formula for the second Melnikov function and theoretical analysis, the following result is obtained: if the first order Melnikov function for a perturbed system is identically equal to zero, and the second order Melnikov function for the perturbed system is not identically equal to zero, the system has at most two limit cycles.