一类五次扰动Hamiltonian系统的Abel积分零点个数

孙宪波

数学学报 ›› 2013, Vol. 56 ›› Issue (6) : 981-992.

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数学学报 ›› 2013, Vol. 56 ›› Issue (6) : 981-992. DOI: 10.12386/A2013sxxb0095
论文

一类五次扰动Hamiltonian系统的Abel积分零点个数

    孙宪波
作者信息 +

The Number of Zeros of Abelian Integral for Some Perturbed Hamiltonian System of Degree 5

    Xian Bo SUN
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摘要

研究一类五次扰动Hamiltonian系统的Abel积分零点个数上界.证明所研究的Abel积分的生成元构成精度为1的Chebeyshev系统,得到Abel积分零点个数上界是4 (考虑零点重数). 并指出前人文献中关于Abel积分零点个数上界的研究存在的错误, 给出了最新结果.

Abstract

We study the number of zeros of the Abelian integral for some perturbed Hamiltonian system of degree 5. We prove the generating elements of the Abelian integral form a Chebeyshev system of accuracy of 1, therefore the number of zeros of the Abelian integral is 4. Last, we show a wrong result given in some previous work about the number of zeros for this Abelian integral, therefore the result we give is very new.

关键词

Abel积分 / Chebeyshev系统 / 弱化Hilbert 16th问题

Key words

Abelian integral / Chebeyshev system / weak Hilbert’s 16th problem

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孙宪波. 一类五次扰动Hamiltonian系统的Abel积分零点个数. 数学学报, 2013, 56(6): 981-992 https://doi.org/10.12386/A2013sxxb0095
Xian Bo SUN. The Number of Zeros of Abelian Integral for Some Perturbed Hamiltonian System of Degree 5. Acta Mathematica Sinica, Chinese Series, 2013, 56(6): 981-992 https://doi.org/10.12386/A2013sxxb0095

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基金

国家自然科学基金资助项目(11261013);广西财经学院校级科研项目(2012C08);广西高校科研项目(2013YB216)

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