一类连续分段线性Hamilton系统在线性扰动下极限环个数的估计  

Estimation of number of limit cycles for a class of continuous piecewise linear Hamiltonian systems under linear perturbation

作　　者：邓蕊 李宝毅[1] 张永康[1] DENG Rui;LI Baoyi;ZHANG Yongkang(College of Mathematical Science,Tianjin Normal University,Tianjin 300387,China)

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）》2020年第3期1-5,共5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：用平行的2条直线将平面分为3个区域,研究一类连续的分段线性Hamilton系统在一次多项式扰动下周期闭轨族附近分支出极限环的个数.通过计算一阶Melnikov函数M1(h),利用Chebyshev系统的性质证明了当M1(h)不恒为0时,该系统在一次连续多项式扰动下极限环个数的上确界为2,在一次非连续多项式扰动下极限环个数的上确界为4.When the plane is divided into three regions by two parallel straight lines,the number of limit cycles bifurcated by a class of continuous piecewise linear Hamiltonian systems in the vicinity of the periodic closed orbit family under linear perturba-tion is studied.By calculating the first-order Melnikov function M1(h)and using the properties of Chebyshev system,it is proved that when M1(h)is not constant to 0,the upper bound of number of limit cycles for the piecewise linear Hamiltonian system is 2 under the continuous perturbation,and the upper bound of number of limit cycles is 4 under the discontinuous perturbation.

关 键 词：连续分段线性Hamilton系统 一次多项式扰动 MELNIKOV函数 Chebyshev系统 极限环 

分 类 号：O175[理学—数学]