Equivalence of the Melnikov function method and the average method
报 告 人:: 韩茂安
报告地点:: 数学与统计学院403室
报告时间:: 2018年01月19日星期五10:20-11:00

There is a folklore about the equivalence between the Melnikov method and the averaging method for studying the number of limit cycles, which are bifurcated from the period annulus of planar analytic differential systems. But there is not a published proof. In this short paper, we prove that for any positive integer k, the kth Melnikov function and the kth averaging function, modulo both Melnikov and averaging functions of order less than k, produce the same number of limit cycles of planar analytic (or C^\infty) near-Hamiltonian systems.

发 布 人:科研助理 发布时间: 2018-01-18