摘要
证明了三次Hamiltonian系统x=2y(b+cx^2+2y^2),y=-2x(a+2x^2+cy^2)在n次多项式扰动下极限环的个数不超过3[n-1/4]+12[n-3/4]+22(计重数),其中a<0,b<0c<-2.
In this paper, we prove that the cyclicity of period annuli for system x= 2y（b ＋ cx^2＋2y^2）,y=2x（a＋2x^2 ＋ cy^2）under perturbations of polynomials with degree n is not more than 3[n-1/4]＋ 12[n-3/4] ＋ 22 （taking into account the multiplicity）, where a 〈 0, b 〈 0 and c 〈 -2.
作者
杨纪华
张二丽
刘媚
YANG Jihua ZHANG Erli LIU Mei(School of Mathematics and Computer Science, Ningxia Normal University, Guyuan, Ningxia, 756000, P. R. China School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, P. R. China School of Information Engineering, Zhengzhou Institute of Finance and Economics, Zhengzhou, Henan, 450001, P. R. China)
出处
《数学进展》
CSCD
北大核心
2017年第2期243-251,共9页
Advances in Mathematics（China）
基金
国家自然科学基金(No.11271046
No.11361046)
宁夏科技支撑计划项目(宁科计字[2015]26号(4))
宁夏自然科学基金(No.NZ13213)
宁夏高等学校科研项目(宁教高[2014]222号(17))
