ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

9. Ordinary Differential Equations and Dynamical Systems

1991 MS Classification: 58, 60 Nguyen, Dinh Cong, Hanoi Institute of Mathematics, Vietnam Structural stability of linear random dynamical systems Investigation of dynamical systems which are influenced by noise leads to a new branch of the theory of dynamical systems. A random dynamical system is a cocycle over a deterministic metric dynamical system which models the noise. A random dynamical system is structurally stable with respect to a random norm if it is topologically conjugate to any system which is sufficiently close to it in this norm. We prove that a linear random dynamical system is structurally stable with respect to its Lyapunov norms if and only if it is hyperbolic. Reference: 1. Nguyen Dinh Cong, Structural stability of linear random dynamical systems, Ergodic Theory and Dynamical Systems, 16(1996), 1207– 1220.

2. Nguyen Dinh Cong, Topological Dynamics of Random Dynamical Systems, Oxford Mathematical Monographs, Clarendon Press, Oxford, 1997.