Random perturbations of fixed points
by
Gunter Ochs
Universität Bremen

We consider random dynamical systems, which model dymamics influenced by noise. Stationary random variables (or equivalently, stationary random Dirac measures) are a generalisation of fixed points of deterministic dynamical systems.

We investigate the influence of small random perturbations on fixed points of deterministic maps. Using results from algebraic ergodic theory we give examples of fixed points which are structurally stable w.r.t. perturbations in the class of deterministic maps but not structurally stable w.r.t. stochastic perturbations.

In particular, we show that topological fixed point theorems like the Brouwer fixed point theorem or theorems based on the Conley index theory cannot be generalized to the case of random dynamical systems.

Date received: January 26, 1996

Copyright © 1996 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caaa-09.