Estimate of the number of zeros of Abelian integrals for a kind of quartic Hamiltonians with two centers

被引：12
|
作者：
Zhou, Xin [1 ]
Li, Cuiping
机构：
[1] Beihang Univ, LMIB, Beijing 100083, Peoples R China
来源：
APPLIED MATHEMATICS AND COMPUTATION | 2008年 / 204卷 / 01期
关键词：
Abelian integral; weakened Hilbert's 16th problem; Picard-Fuchs equation; Hamiltonian system;
D O I：
10.1016/j.amc.2008.06.036
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we give the upper bound of the number of zeros of Abelian integral I(h) =closed integral(Gamma h) P(x,y)dx - Q(x,y)dy, where Gamma(h) is the closed orbit defined by H(x,y)=-chi(2)+ lambda x(4)+y(4)=h, lambda > 0, h epsilon Sigma; Sigma is the maximal open interval on which the ovals {Gamma(h)} exist; P(x,y) and Q(x,y) are real polynomials in x and y of degree at most n. (C) 2008 Elsevier Inc. All rights reserved.
引用
收藏
页码：202 / 209
页数：8
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