一类具多重极限环的二次Hamilton系统的近似系统

Approximate System for Quadratic Hamiltonian System with Multiple Limits

利用Mel’nikov函数,对一类具有以抛物线与直线为边界的周期环域的单中心二次Hamilton系统的三次扰动,分别构造出恰好存在两个单重极限环、恰好存在一个二重极限环、恰好存在一个极限环和一个分界线环的近似系统。

By using Mel＇nikov functions, for the Poincare bifurcation problems of quadratic Hamiltonian system under cubic perturbation with one center and the periodic regions, which has a parabola and an invariant straight line as it＇s bounding. the approximate system to show that there exist just two single limit cycles, or just one double-limit cycle, or just one single-limit cycle and one separatric cycle are given.