Cyclicity of Degenerate Polycycles Through a Saddle-Node and Two Hyperbolic Saddles  

作　　者：Li Qin ZHAO 

机构地区：[1]Department of Mathematics,Beijing Normal University,Beijing 100875,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2005年第3期507-516,共10页数学学报（英文版）

基　　金：Project sponsored by National Science Foundation (19901001)

摘　　要：This paper deals with the cyclicity of a kind of degenerate planar polycycles through a saddle-node and two hyperbolic saddles, where the hyperbolicity ratio of the saddle （which connects the saddle-node with hp-connection） is equal to 1 and that of the other saddle is irrational. It is obtained that the cyclicity of this kind of polycycle is no more than 5 if the hp-connection keeps unbroken under the C^∞ perturbations.This paper deals with the cyclicity of a kind of degenerate planar polycycles through a saddle-node and two hyperbolic saddles, where the hyperbolicity ratio of the saddle （which connects the saddle-node with hp-connection） is equal to 1 and that of the other saddle is irrational. It is obtained that the cyclicity of this kind of polycycle is no more than 5 if the hp-connection keeps unbroken under the C^∞ perturbations.

关 键 词：Degenerate polycycle CYCLICITY Finitely-smooth normal form Transition map 

分 类 号：O18[理学—数学]