平面上含鞍结点与中心型鞍点的余维3环的三参数开折

THE THREE-PARAMETER UNFOLDING OF A KIND OF PLANAR POLYCYCLES WITH A SADDLE-NODE AND A SADDLE OF ZERO SADDLE VALUE

本文应用有限光滑正规形理论研究了含有一个重数为2的鞍结点与一个中心型双曲鞍点（双曲比率为1）的余维3的平面环（Polycycle）的一般三参数开折与环性，证明了这类环至多分支出三条极限环，并且在一般性条件下环性为3，给出了分支图和相应的相图．作为应用，证明了文［4］提出的图（I192）环性为1的猜想．

In this paper we investigate the bifurcation diagrams of the typical threeparameter deformations of a kind of planar polycycles containing a saddle-node of multiplicity two and a hyperbolic saddle with hyperbolicity ratio equal to one. We prove that at most three limit cycles will be generated from this kind of polycycles and the cyclicity is three under some generic conditions. As an application, we prove that the cyclicity of the graph(I192) given in [4] is one.