Bifurcations of Limit Cycles from a Quintic Hamiltonian System with a Heteroclinic Cycle

Bifurcations of Limit Cycles from a Quintic Hamiltonian System with a Heteroclinic Cycle

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摘要 In this paper,we consider Li′enard systems of the form dx/dt=y,dy/dt=x＋bx3-x5＋ε（α＋βx2＋γx4）y,where b∈R,0〈｜ε｜〈〈1,（α,β,γ）∈D∈R3 and D is bounded.We prove that for ｜b｜〉〉1（b〈0） the least upper bound of the number of isolated zeros of the related Abelian integrals I（h）=∮Γh（α＋βx2＋γx4）ydx is 2（counting the multiplicity） and this upper bound is a sharp one. In this paper,we consider Li′enard systems of the form dx/dt=y,dy/dt=x＋bx3-x5＋ε（α＋βx2＋γx4）y,where b∈R,0〈｜ε｜〈〈1,（α,β,γ）∈D∈R3 and D is bounded.We prove that for ｜b｜〉〉1（b〈0） the least upper bound of the number of isolated zeros of the related Abelian integrals I（h）=∮Γh（α＋βx2＋γx4）ydx is 2（counting the multiplicity） and this upper bound is a sharp one.

作者 Li Qin ZHAO De Ping LI

机构地区 School of Mathematical Sciences

出处《Acta Mathematica Sinica,English Series》 SCIE CSCD 2014年第3期411-422,共12页 数学学报（英文版）

基金 Supported by National Natural Science Foundation of China(Grant No.11271046)

关键词 Hyper-elliptic Hamiltonian system Abelian integral period annulus Picard-Fuchs equa-tion Hyper-elliptic Hamiltonian system, Abelian integral, period annulus, Picard-Fuchs equa-tion

分类号 O153.3 [理学—基础数学]

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Acta Mathematica Sinica,English Series

2014年第3期

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Bifurcations of Limit Cycles from a Quintic Hamiltonian System with a Heteroclinic Cycle

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