Random dynamical systems. (Zufällige dynamische Systeme.) (German) Zbl 0805.60048

This paper was given as a presentation at the Jahrestagung der DMV in Berlin, 1992. It provides an overview of the theory of random dynamical systems (RDS’s), and covers in a very short, but precise way the state of the art in the following areas: 1. Metric, topological, and smooth dynamics, 2. RDS: concept, invariant measures, 3. Generation of RDS, 4. The multiplicative ergodic theorem, 5. Invariant manifolds, stability, 6. Normal forms, Grobman-Hartman theorem, 7. Bifurcation theory, 8. Further areas for research. A list of almost 80 references is provided. The author is currently preparing a monograph “Random dynamical systems”, which will present the entire area with all the mathematical details.
Reviewer: W.Kliemann (Ames)


60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
34D08 Characteristic and Lyapunov exponents of ordinary differential equations
34F05 Ordinary differential equations and systems with randomness
93E03 Stochastic systems in control theory (general)