Integral expressions of Lyapunov exponents for autonomous ordinary differential systems

作     者：DAI XiongPing Department of Mathematics, Nanjing University, Nanjing 210093, China 

作者机构：Department of Mathematics Nanjing University Nanjing China 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：2009年第52卷第1期

页      面：195-216页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：supported by the National Natural Science Foundation of China (Grant No. 10671088) the Major State Basic Research Development Program of China (Grant No. 2006CB805903) 

主　　题：Lyapunov spectrum of differential system multiplicative ergodic theorem C 1-vector field smooth linear skew-product flow lifting of probability 34D08 37C10 60B05 37H15 28D10 

摘      要：In the paper, the author addresses the Lyapunov characteristic spectrum of an ergodic autonomous ordinary differential system on a complete riemannian manifold of finite dimension such as the d-dimensional euclidean space ? d , not necessarily compact, by Liaowise spectral theorems that give integral expressions of Lyapunov exponents. In the context of smooth linear skew-product flows with Polish driving systems, the results are still valid. This paper seems to be an interesting contribution to the stability theory of ordinary differential systems with non-compact phase spaces.