On the algebraic structure of Abelian integrals for a kind of perturbed cubic Hamiltonian systems
On the algebraic structure of Abelian integrals for a kind of perturbed cubic Hamiltonian systems
复制标题
DOI：
10.1016/j.jmaa.2009.05.034
复制
发表时间：
2009-11
影响因子：
1.3
通讯作者：
Xin Zhou;Cuiping Li
中科院分区：
文献类型：
--
作者：
Xin Zhou;Cuiping Li
获得了阿贝尔积分的有限生成器[公式：见文本]，其中Γhis由H(x,y)=x2+y2+ax4+bx2y2+cy4= H定义的闭椭圆族，H∈Σ， ac(4ac−b2)≠0，Σ=(0,h1)是开放区间，在该区间上Γhis定义，f(x,y), g（x,y）是x和y中的实数多项式，阶为2n+1 （n大于或等于2）。在特殊情况a>0, b=0, c=1时，由其代数结构给出了阿贝尔积分I(h) 0个数的上界。
The finite generators of Abelian integral [Formula: see text] are obtained, where Γhis a family of closed ovals defined by H(x,y)=x2+y2+ax4+bx2y2+cy4=h, h∈Σ, ac(4ac−b2)≠0, Σ=(0,h1) is the open interval on which Γhis defined, f(x,y), g(x,y) are real polynomials in x and y with degree 2n+1 (n⩾2). And an upper bound of the number of zeros of Abelian integral I(h) is given by its algebraic structure for a special case a>0, b=0, c=1.