Applications of non-linear methods in astronomy

Abstract

In this review I discuss catastrophes, bifurcations and strange attractors in a non-mathematical manner by giving very simple examples that st ill contain the essence of the phenomenon. The salientresults of the applications of these non-linear methods in astrophysics are reviewed and include such diverse phenomena as solar flares and loop brightenings (catastrophes), formation of binaries and cyclic stellar winds (bifurcations) and the solar cycle and galactic dynamics (strange attractors). Emphasis is laid on the unifying concept of non-linearity in (simple) differential equatio ns that can be the framework for understanding and predicting such diverse phenomena as mentioned above. Finally there is a discussion on the concept of intrinsic unpredictability (as a result on non-linearity), the limit it sets to the use of numerical models and the way it contradicts our intuiti ve notions on deterministic systems.