GOODSTEIN ALGORITHM AS A SUPER-TRANSIENT DYNAMICAL SYSTEM

We point out that the Goodstein algorithm may be viewed as a prototype of a novel class of dynamical systems which are characterized by extr emely long transients and a very simple global attractor, and show tha t in addition it possesses super-sensitive dependence on initial condi tions. This radically different mix of features from those usually ass umed within the strange attractor framework could have ramifications f or the way dynamical behaviour is perceived both in theory and in prac tice.