连结平面奇点轨线的存在性

Exsitence of Trajectories Connecting Plane Critical Points

对C1平面流f,如果存在点p0∈R2及奇点p1,p2,使得limt→+∞f(p0,t)=p1,limt→-∞f(p0,t)=p2,称f(p0,R)是连结奇点p1,p2的轨线。利用连结弧的半有界性,得到了一些判别仅含2个奇点的平面动力系统连结轨线存在的准则。

For C^1 plane flow f, we call f(p_0,R) the trajectory connecting p_1,p_2, if there exist point p_0∈R^2 and two singular points p_1,p_2,such that (limt→+∞)f(p_0,t)=p_1,(limt→-∞)f(p_0,t)=p_2. With half-bounded connecting arc, some criteria for the existence of trajectories connecting a pair of critical points of planar dynamitic systems are given.