一类Hamiltonian系统的Abel积分的零点个数估计

数学季刊 ›› 2005, Vol. 20 ›› Issue (2): 158-162.

一类Hamiltonian系统的Abel积分的零点个数估计

Department of Mathematics, Bohai University, Jinzhou 121000, China

收稿日期:2002-11-05 出版日期:2005-06-30 发布日期:2024-01-22
作者简介:SONG Yan(1962-),female(Manzu),native of Jinzhou,Liaoning,an associate professor of Bohai University,M.S.D.,engages in qualitative theory of ordinary differential equations.
基金资助:

The Estimation of the Number of Zeros of the Abelian Integrals for a Class of Hamiltonian Systems

Department of Mathematics, Bohai University, Jinzhou 121000, China

Received:2002-11-05 Online:2005-06-30 Published:2024-01-22
About author:SONG Yan(1962-),female(Manzu),native of Jinzhou,Liaoning,an associate professor of Bohai University,M.S.D.,engages in qualitative theory of ordinary differential equations.

摘要/Abstract

摘要： In this paper,we discuss the estimation of the number of zeros of the Abelian integral for the quadratic system which has a periodic region with a parabola and a straight line as its boundary when we perturb the system inside the class of all polynomial systems of degree n.The main result is that the upper bound for the number of zeros of the Abelian integral associated to this system is 3n-1.

关键词: Hamiltonian , , system;Abelian , , integral;Picard-Fuchs , , equation;general , , Rolle's theorem

Abstract: In this paper,we discuss the estimation of the number of zeros of the Abelian integral for the quadratic system which has a periodic region with a parabola and a straight line as its boundary when we perturb the system inside the class of all polynomial systems of degree n.The main result is that the upper bound for the number of zeros of the Abelian integral associated to this system is 3n-1.

Key words: Hamiltonian , , system;Abelian , , integral;Picard-Fuchs , , equation;general , , Rolle's theorem

中图分类号:

O175

宋燕. 一类Hamiltonian系统的Abel积分的零点个数估计[J]. 数学季刊, 2005, 20(2): 158-162.

SONG Yan . The Estimation of the Number of Zeros of the Abelian Integrals for a Class of Hamiltonian Systems[J]. Chinese Quarterly Journal of Mathematics, 2005, 20(2): 158-162.

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