一类Z_(2)等变Hamilton向量场在分段低次多项式扰动下极限环个数的估计  

Number of limit cycles bifurcating from a class of Z_(2)-equivariant Hamiltonian systems perturbed by piecewise low-order polynomials

作　　者：曾慧 李宝毅[1] 张永康[1] ZENG Hui;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）》2022年第3期11-16,共6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);2020年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Z_(2)等变Hamilton向量场,当平面分为左右2个区域时,基于二阶微分算子法和广义Rolle定理讨论该系统的周期闭轨族在分段非连续(连续)n次多项式扰动下(n=1、2、3)极限环的个数,当一阶Melnikov函数不恒为0时,得到了该系统分支出极限环个数的上确界B(n)(B_(c)(n))(计重数).A class of Z_(2)-equivariant Hamiltonian systems is considered.When the plane is divided into left and right regions,the second-order differential operators and the generalized Rolle theorem are used to estimate the number of limit cycles bifurcating from period annuli perturbed by piecewise(continuous)low-order polynomials.If the first order Melnikov function is not equal to zero identically,the least upper bounds of number of limit cycles B(n)(B_(c)(n))are obtained.

关 键 词：Z_(2)等变向量场 HAMILTON系统 极限环 二阶微分算子 广义Rolle定理 

分 类 号：O175[理学—数学]