半稳定环的不存在性

The Non-existence of Semi-stable limit Cycle

本文将半稳定环存在的必要条件加以变形,使之含有一个可供选择的任意常数。利用这个新的必要条件得到若干半稳定环不存在的判别法,其中包括在单个奇点外围不存在半稳定环的条件,在两个奇点外围不同时存在半稳定环的条件,以及在两个奇点外围均不存在半稳定环的条件。

New sufficient conditions are obtained for the non-existence of semi-stable limit cycle. The results in this paper include the conditions that semi-stable limit cycles do not exist around one focus or another, semi-stable limit cycles do not exist around two focus, and non semi-stable limit cycles exist around any focus.