中文摘要：

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．

英文摘要：

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.