平面上含两鞍结点和一鞍点的余维三多角环的三参数开折

The Three-parameter Unifoldings of Several Kinds of Planar Polycycles with Two Saddle-nodes and One Saddle

本文应用有限光滑正规形理论，研究了平面上含有两个重数为２的鞍结点和一个双曲比率≠１的双曲鞍点的三类余维三多角环的一般三参数开折．证明了这三类多角环至多能分支出三条极限环，给出了分支图．

In this paper we investigate the bifurcation diagrams of the general three-parameter deformations of three kinds of planar polycycles and ensembles containing two saddle-nodes of multiplicity two and one hyperbolic saddle with hyperbolicity ratio different from 1. We prove that at most three limit cycles will be generated from these kinds of polycycles and ensembles.