Professor Ludwig Arnold, Bremen Univ, Germany
The Middle Lecture Room, Math Building
We first discuss the general concept of a dynamical system, with examples in ergodic theory, topological and smooth dynamics. Then we define a random dynamical system (RDS). The definition is tailor-made to cover all important systems under randomness which are presently of interest. Examples are products of random mappings and random and stochastic differential equations. Invariant measures for RDS are introduced. The basic Multiplicative Ergodic Theorem (Oseledets 1968) is presented. This random substitute of linear algebra enables us to do “local theory” of nonlinear RDS: Stability, invariant manifolds, normal forms, stochastic bifurcation, etc. Random attractors are introduced and Lyapunov’s second method for RDS is presented.