极限集中关于无切线段的分析

通过对自治系统轨线极限集和自治系统无切线段的分析,得到轨线与该轨线极限集中点的关系。为了寻找轨线与此极限集中任意点的关系,首先根据极限集具体情况(极限集中是否只有奇点),将所研究问题划分为两种情况进行讨论。根据轨线是否经过该轨线极限集,找到在每一种情况下轨线或者属于极限集或者无限趋近于极限集中的点。对轨线极限集含有常点的轨线而言,经过该轨线极限集任意常点,必然存在自治系统一条无切线段或者与该轨线有可列个交点或者轨线经过极限集的常点。

By analyzing the limit set of autonomous system trajectories and the non tangent segment of autonomous system,the relationship between the trajectory and the limit point of the trajectory is obtained.ln order to find the relationship between the trajectories and the limit points,first of all,according to the specific conditions of the limit set （is there only a singularity- in the limit eoneentration）,the research problems are divided into two eases. According to whether the track line passes the limit set of the trajeetory,we found the track line either belong to a limit set or infinitely close to a point of the limit set. Further discussion is concerned with the trajectories of the limit set with constant points.Through the limit set of the trajectories arbitrary points,a regular point of an autonomous system that has a non tangent line segment or an intersection with the track or the track line passes the limit set.