高维Kramers系统的奇点分析  

The Analysis of Critical Points of Kramers System in High Dimension

作　　者：程艳峰[1] 包立平[1] 

机构地区：[1]杭州电子科技大学理学院,浙江杭州310018

出　　处：《杭州电子科技大学学报（自然科学版）》2009年第2期96-98,共3页Journal of Hangzhou Dianzi University：Natural Sciences

摘　　要：该文讨论了二维Kramers问题的奇点问题,得到了相应的奇点分类,讨论了奇点的稳定性与形变位能极值的关系,得出稳定奇点必为位能极小值点,第二类鞍点必为位能极大值点。该文证明了Kramers系统无闭轨,孤立奇点的吸引域必为单连通开集,并得出吸引域边界上的点出发的轨线的ω-极限点必为系统的鞍点或焦鞍点。In this paper,points of two-dimensional Kramers system are analyzed.The classification of the critical points is obtained.The relationship between the stability of the equilibrium points of the system and extreme points of the potential function is considered.It is found that:(i) the stable critical points are the minimum points of the potential function,and(ii) the type II saddle points are the maximum points of the potential function.The domain of attraction of the isolated stable equilibrium point is ope...

关 键 词：克莱默斯系统 奇点 稳定性 形变位能 吸引域 

分 类 号：O175.12[理学—数学]