307
个编辑
更改
无编辑摘要
By the Jordan curve theorem, every closed trajectory divides the plane into two regions, the interior and the exterior of the curve.
By the Jordan curve theorem, every closed trajectory divides the plane into two regions, the interior and the exterior of the curve.
通过'''<font color="#ff8000">若尔当曲线定理 Jordan Curve Theorem</font>'''，每一个封闭的轨迹将平面分成两个区域，内部和外部的曲线。
Given a limit cycle and a trajectory in its interior that approaches the limit cycle for time approaching <math>+ \infty</math>, then there is a neighborhood around the limit cycle such that all trajectories in the interior that start in the neighborhood approach the limit cycle for time approaching <math> + \infty</math>. The corresponding statement holds for a trajectory in the interior that approaches the limit cycle for time approaching <math>- \infty</math>, and also for trajectories in the exterior approaching the limit cycle.
Given a limit cycle and a trajectory in its interior that approaches the limit cycle for time approaching <math>+ \infty</math>, then there is a neighborhood around the limit cycle such that all trajectories in the interior that start in the neighborhood approach the limit cycle for time approaching <math> + \infty</math>. The corresponding statement holds for a trajectory in the interior that approaches the limit cycle for time approaching <math>- \infty</math>, and also for trajectories in the exterior approaching the limit cycle.
给定一个极限环和它内部在时间上趋近<math>+ \infty</math>的接近极限环的轨迹，在极限环周围有一个邻域，这样所有内部开始的轨迹在时间上趋近<math> + \infty</math>时都接近极限环。相应的陈述适用于时间上趋近<math>- \infty</math>的接近极限环的内部轨道，也适用于接近极限环的外部轨道。