测地流上的封闭周期轨道的渐近扩张  

Asymptotic expansion for closed orbits of geodesic flows

作　　者：刘亚丽[1] 

机构地区：[1]南京理工大学理学院,江苏南京210000

出　　处：《湖北师范学院学报（自然科学版）》2016年第4期22-27,共6页Journal of Hubei Normal University(Natural Science)

摘　　要：黎曼流形上的双曲流或Anosov流的闭轨道是一些常见的动力系统的周期运动的像。例如测地流就是一种特殊的双曲流,而闭测地线可以看作是测地流的闭轨道。得到了负曲率流形上的闭测地线的渐近形式.对于一对闭测地线,若它们的轨道长度之差位于一个已知的区间内,且它们的字长都等于一个定值,而对于满足这些条件的闭测地线的渐近问题,是文章的主要研究内容。The closed orbits of hyperbolic or Anosov flows on Riemann manifolds are the images of the periodic motion of some common dynamical systems. For example, the geodesic flow is a special double flow, and closed geodesics can be regarded as a closed orbit of the geodesic flows. In this paper we obtain asymptotic estimates for pairs of closed geo- desics on negatively curved manifolds. For a pair of closed geodesics,the differences of whose lengths lie in a prescribed shrinking intervals and their length are equal to a constant value. And researching the asymptotic question for which pairs of geodesics meeting these aboving conditions is the main content of this article.

关 键 词：测地线 傅里叶变换 测地流 符号动力系统 

分 类 号：O19[理学—数学]