空间系统鞍焦点同宿环的稳定性  

Stability of Homoclinic Cycles to a Saddle-focus in Space System

作　　者：黄璇[1] 王丽英[2] 

机构地区：[1]井冈山大学数理学院数学系,江西吉安343009 [2]张家口职业技术学院基础部,河北张家口075000

出　　处：《山西大学学报（自然科学版）》2009年第2期172-176,共5页Journal of Shanxi University(Natural Science Edition)

基　　金：国家自然科学基金(106471069)

摘　　要：文章在可定义回复映射的条件下,按照Wiggins在文献[2]中介绍的构造Poincaré映射的方法,给出了空间系统鞍焦点同宿环在其部分邻域中是渐近稳定或不稳定的判据.The stability of homoclinic cycles connecting a saddle in R^3 was discussed in paper[1], but there has little paper concerning about the stability of homoclinic cycle to a saddle-focus. Based on establishing the recurrent map by the method introduced in [2], a criterion for the asymptotic stability of homoclinie cy- cles to a saddle-focus in R^3 is given.

关 键 词：空间系统 鞍焦点 同宿环 渐近稳定 回复映射 

分 类 号：O175.13[理学—数学]