Perturbations of a class of hyper-elliptic Hamiltonian systems of degree seven with nilpotent singular points

Xianbo Sun and Liqin Zhao

Applied Mathematics and Computation, 2016, vol. 289, issue C, 194-203

Abstract: In this paper, we study the number of isolated zeros of Abelian integrals associated to system x˙=y,y˙=−x3(x2−1)2 under the perturbations of ϵ(α0+α1x2+α2x4+α3x6)y∂∂y, where 0 < |ϵ| ≪ 1 and αi ∈ R(i=0,1,2,3). We find a special transformation such that four generating elements are reduced to special three ones and then the algebraic method can be used. The bounds and sharp bounds are obtained.

Keywords: Limit cycle; Abelian integral; Nilpotent singular point; Hyper-elliptic Hamiltonian system; Heteroclinic loop (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:289:y:2016:i:c:p:194-203

DOI: 10.1016/j.amc.2016.04.018

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