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

作     者：Li Qin ZHAO De Ping LI 

作者机构：School of Mathematical SciencesBeijing Normal UniversityLaboratory of Mathematics and Complex SystemsMinistry of Education 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2014年第30卷第3期

页      面：411-422页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：Supported by National Natural Science Foundation of China(Grant No.11271046) 

主　　题：Hyper-elliptic Hamiltonian system Abelian integral period annulus Picard-Fuchs equa-tion 

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 *** 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.