两类扰动的1形式二次可逆中心阿贝尔积分的零点个数  

On the number of zeros for Abelian integrals in two perturbed quadratic reversible centers of genus one

作　　者：洪丽君 刘金灵 洪晓春[3] Hong Lijun;Liu Jinling;Hong Xiaochun(School of Mathematics,Sun Yat-sen University,Guangzhou 510275,China;School of Statistics and Mathematics,Zhongnan University of Economics and Law,Wuhan 430073,China;School of Statistics and Mathematics,Yunnan University of Finance and Economics,Kunming 650221,China)

机构地区：[1]中山大学数学学院,广东广州510275 [2]中南财经政法大学统计与数学学院,湖北武汉430073 [3]云南财经大学统计与数学学院,云南昆明650221

出　　处：《纯粹数学与应用数学》2022年第4期452-462,共11页Pure and Applied Mathematics

基　　金：国家自然科学基金(11761075)。

摘　　要：对于两类亏格1形式的二次可逆系统(r19)和(r20),使用Riccati方程方法,研究了它们在任意3,2,1次多项式扰动下的阿贝尔积分孤立零点个数的上界.获得的结果是:对于系统(r19),在3次或2次多项式扰动下,上界是5,在1次多项式扰动下,上界是1;对于系统(r20),在3次多项式扰动下,上界是5,在2次或1次多项式扰动下,上界是4.这些结果是对之前结果的改进.For two kinds of quadratic reversible central systems of genus one(r19)and(r20)under arbitrary triple degree,quadratic degree,or linear polynomial perturbations,we use the Riccati equation method to study the upper bound of the number of isolated zeros of their Abelian integral.The results are as follows:for system(r19),the upper bound is 5 under triple degree or quadratic degree polynomial perturbations,and the upper bound is 1 under linear polynomial perturbations;for system(r20),the upper bound is 5 under the cubic polynomial perturbation,and the upper bound is 4 under the quadratic or first polynomial perturbation.These results are an improvement on the previous results.

关 键 词：阿贝尔积分 二次可逆系统 极限环 RICCATI方程 

分 类 号：O175.12[理学—数学]