This paper is devoted to studying smooth normal form theory of hyperbolic vector fields. As a continuation of our previous work on smooth classification and linearization of vector fields near a hyperbolic singular po...This paper is devoted to studying smooth normal form theory of hyperbolic vector fields. As a continuation of our previous work on smooth classification and linearization of vector fields near a hyperbolic singular point,in this paper,we deal with the case of hyperbolic vector fields on R3 by examining all possible resonant classes.展开更多
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 NSFC under Grant No.10601004Beijing Natural Science Foundation underGrant No.1072002Youthful Teachers Funds of Beijing University of Technology under GrantNo.97006012200601
文摘This paper is devoted to studying smooth normal form theory of hyperbolic vector fields. As a continuation of our previous work on smooth classification and linearization of vector fields near a hyperbolic singular point,in this paper,we deal with the case of hyperbolic vector fields on R3 by examining all possible resonant classes.
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.
