一类三次Hamilton系统的极限环分支

Acta mathematica scientia,Series A ›› 2017, Vol. 37 ›› Issue (5): 825-833.

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Limit Cycle Bifurcations for a Kind of Hamilton Systems of Degree Three

Zhang Erli¹, Xing Yuqing²

1. School of Information Engineering, Zhengzhou Institute of Finance and Economics, Zhengzhou 450044;
2. College of Sciences, Henan Agricultural University, Zhengzhou 450002

Received:2017-01-13 Revised:2017-04-16 Online:2017-10-26 Published:2017-10-26
Supported by:
Supported by the Key Program of Higher Education of Henan (16A110038, 17B110003) and the Cultivating Backbone Teachers Program of Higher Education of Henan (2016GGJS-190)

Abstract

Abstract: By using the Picard-Fuchs equation method, we obtain an upper bound of the number of zeros of Abelian integrals I(h)=∫_{Γ_h}g(x,y)dx-f(x,y)dy, where Γ_h is the closed orbit defined by H(x,y)=x²+y²+2xy+1/a(x⁴+y⁴)=h, a>0,h∈(0,+∞),f(x,y) and g(x,y) are real polynomials in x and y of degree n. Therefore, we get the upper bound of the number of limit cycles of this system.

Key words: Hamilton system, Abelian integrals, Picard-Fuchs equation, Limit cycle

CLC Number:

O175

Zhang Erli, Xing Yuqing. Limit Cycle Bifurcations for a Kind of Hamilton Systems of Degree Three[J].Acta mathematica scientia,Series A, 2017, 37(5): 825-833.

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Limit Cycle Bifurcations for a Kind of Hamilton Systems of Degree Three

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