We discuss various methods and problems pertaining to that part of Random Dynamical Systems which deals with real noise processes. We consider the theory of random orthogonal polynomials, and show how methods applied to the study of the random Schrodinger operator can be generalized to study them. We further discuss certain questions in the area of random bifurcation theory; we formulate and illustrate a “robustness” criterion pertaining to bifurcation in the presence of real noise. Finally, we give a brief survey of some other recent advances in the field.
We study bifurcations in dynamical systems with bounded random perturbations. Such systems, which arise quite naturally, have been nearly ignored in the literature, despite a rich body of work on systems with unbounded, usually normally distributed, noise. In systems with bounded random perturbations, new kinds of bifurcations that we call ‘hard’ may happen and in fact do occur in many situations when the unperturbed deterministic systems experience elementary, codimension-one bifurcations such as saddle-node and homoclinic bifurcations. A hard bifurcation is defined as discontinuous change in the density function or support of a stationary measure of the system.
Berzelius failed to make use of Faraday's electrochemical laws in his laborious determination of equivalent weights.