Instabilities and Nonequilibrium Structures IV

We have classified the articles presented here in two Sections according to their general content.

In Part I we have included papers which deal with statistical mechanics, math- ematical aspects of dynamical systems and sthochastic effects in nonequilibrium systems.

Part II is devoted mainly to instabilities and self-organization in extended nonequilibrium systems.

The study of partial differential equations by numerical and analytic methods plays a great role here and many works are related to this subject.

Most recent developments in this fascinating and rapidly growing area are discussed.

PART I STATISTICAL MECHANICS AND RELATED TOPICS NONEQUILIBRIUM POTENTIALS FOR PERIOD DOUBLING R.

Graham and A. Hamm Fachbereich Physik, Universitiit Gesamthochschule Essen D4300 Essen 1 Germany ABSTRACT.

In this lecture we consider the influence of weak stochastic perturbations on period doubling using nonequilibrium potentials, a concept which is explained in section 1 and formulated for the case of maps in section 2.

In section 3 nonequilibrium potentials are considered for the family of quadratic maps (a) at the Feigenbaum 'attractor' with Gaussian noise, (b) for more general non- Gaussian noise, and (c) for the case of a strange repeller.

Our discussion will be informal. A more detailed account of this and related material can be found in our papers [1-3] and in the reviews [4, 5], where further references to related work are also given. 1.