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

Chinese Quarterly Journal of Mathematics ›› 2005, Vol. 20 ›› Issue (2): 158-162.

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.

Abstract

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

CLC Number:

O175

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

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