一类3维反转系统中的异维环分支  

Heterodimensional Cycle Bifurcations in a 3-Dimensional Reversible System

作　　者：邓桂丰[1] 刘福窑[1] 路秋英[2] 张伟鹏[3] 

机构地区：[1]上海立信会计学院数学与信息学院,上海2016202 [2]浙江理工大学数学系,杭州310018 [3]东北师范大学数学与统计学院,长春130024

出　　处：《数学年刊（A辑）》2013年第4期401-414,共14页Chinese Annals of Mathematics

基　　金：国家自然科学基金(No.11101283;No.11178014;No.11101370;No.11001041);上海市教育委员会科研创新基金(No.12YZ173)的资助

摘　　要：研究了一类3维反转系统中包含2个鞍点的对称异维环分支问题,且仅限于研究系统的线性对合R的不变集维数为1的情形.给出了R-对称异宿环与R-对称周期轨线存在和共存的条件,同时也得到了R-对称的重周期轨线存在性.其次,给出了异宿环、同宿轨线、重同宿轨线和单参数族周期轨线的存在性、唯一性和共存性等结论,并且发现不可数无穷条周期轨线聚集在某一同宿轨线的小邻域内.最后给出了相应的分支图.The authors study the bifurcations of symmetric heterodimensional cycles with two saddle points in 3-dimensional reversible system when the fixed points space of the linear involution R is 1-dimensional. Firstly the existence and coexistence of R-symmetric heteroclinic loop and R-symmetric periodic orbit are obtained. The double R-symmetric periodic orbit is also found. Secondly the authors present sufficient conditions for the existence, uniqueness and coexistence of heteroclinic loop, homoclinic loops, double homoclinic loop and a single-parameter family of periodic orbits. It is shown that infinitely many periodic orbits accumulate along a homoclinic loop. Moreover, the bifurcation surfaces and their existence regions are located.

关 键 词：异维环 反转系统 异宿分支 活动标架 

分 类 号：O175[理学—数学]