一类平面分段线性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 planar piecewise linear Hamiltonian systems under linear perturbations

作　　者：赵凌燕 李宝毅[2] 张永康[2] ZHAO Lingyan;LI Baoyi;ZHANG Yongkang(Air Force Early Warning Academy,Wuhan 430019,China;College of Mathematical Science,Tianjin Normal University,Tianjin 300387,China)

机构地区：[1]空军预警学院,武汉430019 [2]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）》2021年第6期1-7,共7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);天津市普通高等学校本科教学质量与教学改革研究计划项目(B201006505).

摘　　要：考虑一类平面分段线性Hamilton系统.当平面被从原点出发的射线分为2m-1(m≥2)个区域时,研究该系统在线性扰动下极限环的个数,运用一阶Melnikov函数及Taylor展开证明了扰动系统至少存在3 m个极限环.A class of planar piecewise linear Hamiltonian systems is considered.When the plane is divided into 2m-1(m≥2)regions by the rays from the origin,the number of limit cycles for the Hamiltonian systems under linear perturbations is studied.It is proved that the number of limit cycles for the perturbation systems is at least 3m using the first order Melnikov function and Taylor expansion.

关 键 词：平面分段线性Hamilton系统 线性扰动 一阶Melnikov函数 TAYLOR展开 极限环 

分 类 号：O175[理学—数学]