Integral expressions of Lyapunov exponents for autonomous ordinary differential systems  

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

出　　处：《Science China Mathematics》2009年第1期195-216,共22页中国科学：数学（英文版）

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)

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.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 Rd, 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.

关 键 词：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 

分 类 号：O175[理学—数学]