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

Yang Jihua1, Zhang Erli2   

  1. 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 Revised:2018-12-07 Published:2019-11-08
  • Supported by:
    Supported by the NSFC (11701306, 11601250), the Construction of First-class Disciplines of Higher Education of Ningxia (pedagogy) (NXYLXK2017B11) and the Young Top-Notch Talent of Ningxia and Training Plan of University Young Key Teacher of Henan Province (2017GGJS202, 2016GGJS190)

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