This collection of review articles is aimed at those with some background knowledge of Dynamical Systems Theory. It will be useful to graduate students and researchers wishing to familiarize themselves with current research, as well as to those currently working in the field.

Each of the authors has given a survey of an active research topic. The aim is to provide a useful review of the directions in which particular lines of research are going, together with a wide list of references for further reading, and to provide the reader with a number of open problems.

This book is loosely associated with the conference on “Theoretical and Numerical Problems in the Study of Chaotic Ordinary Differential Equations” held at King's College, Cambridge in June and July 1986. The conference was funded by the S.E.R.C. and the Dynamical Systems Project of King's College Research Centre.

The Editors would like to thank David Tranah and Martin Gilchrist at C.U.P., and Ben Mestel and Colin Sparrow of the King's College Research Centre for their help and advice. We are also grateful to Klaus Schmidt and Ian Stewart for letting us use the mathematical fonts they developed for the Apple Macintosh Computer.