四维系统中同宿流形的非共振同宿分支  

Nonresonant Homoclinic Bifurcations in the Homoclinic Manifold for the 4-Dimensional System

作　　者：王言芹[1] 朱德明[2] 

机构地区：[1]江苏工业学院信息科学系,江苏常州213106 [2]华东师范大学数学系,上海200062

出　　处：《山西大学学报（自然科学版）》2006年第4期352-358,共7页Journal of Shanxi University(Natural Science Edition)

基　　金：国家自然科学基金(1037104)

摘　　要：考虑四维系统中由一族同宿轨道组成的同宿流形{Γ(α)}在非共振条件下的同宿分支.利用局部坐标系,通过建立Po incaré映射和后继函数,分别得出在相应于α=-α的同宿轨道{Γ(-α)}附近存在1-周期轨道和1-同宿轨道的条件,并得到相应的分支曲面的近似表达式,推广了已有的结果.The homocinic bifurcations under the nonresonant conditions are considered in the homoclinic manifold consisting of a series of homoclinic orbits Γ（α）,α∈I include R for the 4-dimensional system. By using local coordinates transformation,Poincar6 map and Subsequent function were built. The existence,uniqueness and incoexistence of 1-homoclinic orbit and 1-periodic orbit were obtained under the nonresonant condition. Moreover, the approximate expressions of the corresponding bifurcation surfaces were given. Some results in the literatures were extended.

关 键 词：局部坐标 POINCARÉ映射 同宿轨道 周期轨道 非共振条件 

分 类 号：O175.12[理学—数学]