一类平面分段光滑线性Hamilton系统在多项式扰动下的极限环个数  

Number of limit cycles for a class of planar piecewise smooth linear Hamiltonian systems under polynomial perturbation

作　　者：程振峰 李宝毅[1] 张永康[1] CHENG Zhenfeng;LI Baoyi;ZHANG Yongkang(College of Mathematical Science, Tianjin Normal University, Tianjin 300387, Chin)

机构地区：[1]天津师范大学数学科学学院,天津300387

出　　处：《天津师范大学学报（自然科学版）》2018年第3期1-4,共4页Journal of Tianjin Normal University：Natural Science Edition

基　　金：国家自然科学基金资助项目(11271046;11671040);天津师范大学博士基金资助项目(52XB1414)

摘　　要：研究一类平面抛物-椭圆型分段光滑线性Hamilton系统在n次多项式扰动下的极限环个数.计算得到系统一阶Melnikov函数的表达式,利用广义罗尔定理证明了该类平面抛物-椭圆型分段光滑线性Hamilton系统在n次多项式扰动下极限环个数的上界为n-1+2[(n+1)/2].The number of limit cycles for a class of planar piecewise smooth linear parabolic-elliptic Hamiltonian systems under polynomial perturbation of degree n is studied. By calculating the expression of the first order Melnikov function and applying generalized Rolle theorem,it is proved that the upper bound of limit cycles for this planar piecewise smooth linear systems is n-1 ＋ 2[（n ＋ 1）/2].

关 键 词：分段光滑线性系统 HAMILTON系统 MELNIKOV函数 广义罗尔定理 极限环 

分 类 号：O175.12[理学—数学]