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 s...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.展开更多
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)
文摘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.
