一类1:2共振的Hamilton系统在分段n次多项式扰动下Abel积分的零点个数  

Number of zeros of Abelian integrals perturbed by piecewise n-degree polynomials for a class of Hamiltonian systems with 1:2 resonance

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）》2021年第4期24-30,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);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1:2共振的Hamilton系统,利用Melnikov函数法和广义Rolle定理证明了当平面分为左右2个区域时,该系统的周期闭轨族Γ_(h)在分段n(≥2)次多项式扰动下的Abel积分I(h)的孤立零点个数不超过2n+7[n/2]+1(计重数).A class of Hamiltonian systems with 1:2 resonance is considered.By using the Melnikov function method and the generalized Rolle theorem,it is proved that when the plane is divided into left and right regions,the number of isolated zeros of Abelian integrals I(h)are not exceed 2n+7[n/2]+1 with multiplicities accounted,where I(h)along closed orbits Γ_(h) of the systems perturbed by piecewise n-degree polynomials,n≥2.

关 键 词：1:2共振 HAMILTON系统 ABEL积分 广义Rolle定理 

分 类 号：O175[理学—数学]