一类可逆二次系统的Abel积分与临界周期  

Abelian integrals and critical periods for a class of reversible quadratic systems

作　　者：洪春[1] 邹兰[1] 

机构地区：[1]四川大学数学学院,成都610064

出　　处：《四川大学学报（自然科学版）》2012年第5期960-964,共5页Journal of Sichuan University(Natural Science Edition)

基　　金：四川大学青年教师科研启动基金(2010SCU11079);数学天元青年基金(11126230)

摘　　要：作者研究了一类平面可逆二次系统的Abel积分和临界周期,得到该系统的Abel积分满足一个Picard-Fuchs方程,进而把系统的临界周期问题化成了一个Riccati方程解的零点判定问题,并最终用Abel积分方法得到了该系统具有等时中心和周期函数周期单调递增的条件.The authors investigate Abelian integrals and critical periods of a class of reversible quadratic systems in the paper. The Picard-Fuchs equation is derived by the Abelian integrals of this reversible quadratic system. Moreover, the problem of critical periods is turned into the problem of determining the number of zeros for the solution of a Riccati equation. Finally, by the way of Abelian integrals, conditions of isochronous center and that of an increasing period function for the reversible quadratic system are given respectively.

关 键 词：ABEL积分 临界周期 PICARD-FUCHS方程 

分 类 号：O175.1[理学—数学]