四维空间中的异维环分支问题

Bifurcations of Heterodimensional Cycles in R^4

利用局部活动坐标架法,讨论了四维空间中连接两个鞍点的异维环分支问题,在一些通有的假设下,分别得到了异维环保存、同宿环、周期轨存在的充分条件以及保存的异维环与分支出的周期轨共存(或不共存)的结果.

Bifurcations of heterodimensional cycles connecting two saddles in R^4 are stud- ied using local active coordinates. Under some generic conditions, the authors obtain the persistence of the heterodimensional cycle, existence of one homoclinic loop and one periodic orbit, coexistence （resp. noncoexistence） of the persistent heterodimensional cycle with the bifurcated periodic orbit.