一类Hamiltonian系统的Abelian积分的零点

Acta mathematica scientia,Series A ›› 2019, Vol. 39 ›› Issue (5): 1025-1032.

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Zeros of Abelian Integral for a Kind of Hamiltonian Systems

Jihua Yang^1,*(),Erli Zhang²

¹ School of Mathematics and Computer Science, Ningxia Normal University, Ningxia Guyuan 756000
² School of Information Engineering, Zhengzhou Institute of Finance and Economics, Zhengzhou 450001

Received:2018-08-05 Online:2019-10-26 Published:2019-11-08
Contact: Jihua Yang E-mail:jihua1113@163.com
Supported by:
the NSFC(11701306);the NSFC(11601250);the Construction of First-class Disciplines of Higher Education of Ningxia (pedagogy)(NXYLXK2017B11);the Young Top-Notch Talent of Ningxia and Training Plan of University Young Key Teacher of Henan Province(2017GGJS202);the Young Top-Notch Talent of Ningxia and Training Plan of University Young Key Teacher of Henan Province(2016GGJS190)

Abstract

Abstract:

In this paper, we obtain an upper bound of the number of zeros of Abelian integral for a kind of Hamiltonian systems. The Abelian integral has k + 2 generators which satisfy two different Picard-Fuchs equations. Finally, we present two examples to illustrate an application of the theoretical result.

Key words: Hamiltonian system, Abelian integral, Picard-Fuchs equation, Chebyshev space, Hilbert-Arnold problem

CLC Number:

O175

Jihua Yang,Erli Zhang. Zeros of Abelian Integral for a Kind of Hamiltonian Systems[J].Acta mathematica scientia,Series A, 2019, 39(5): 1025-1032.

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References 8

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Zeros of Abelian Integral for a Kind of Hamiltonian Systems

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