In a journey of reminiscent impressions, let us first recall the scientific evolution of our institute that led to the initiation of our work on chaos. It is not an isolated piece of research of the ICA but forms an integral part of the philosophy of our work.

As the reader will have been informed through our previous writings, the intensive research which was executed originally at the Department of Aeronautics at Impe­rial College was continued from 1959 to 1984 at the ISD (Institute of Statics and Dynamics of Aerospace Structures) of the University of Stuttgart. This span of time initiated inter alia the revolution of the Finite Element Method. Our research was initially motivated by the intellectually and technically complex demands of aeronautics and astronautics. Although the main effort was directed originally towards problems in astronautical structures, this was by no means the rule, and considerable attention was paid to problems arising in oil tankers and suspension roofs as well as other unusual complex engineering configurations. Moreover, from the mid-Sixties, a further diversification of research led to innovative applications of computer methods in aerodynamics, lubrication, heat transfer, radiation, elec­tromagnetic theory and other field problems. Indeed, with the emergence of vector computers as well as parallel computers, the ICA initiated a number of novel al­gorithmic techniques and directed its attention to new problems in physics such as that of soliton waves and the analysis of ceramic coatings.

For all the industrial and physical topicality of these investigations, we believe, however, that the most exciting research effort at the ICA is concerned with the theory and application of chaotic manifestations in non-linear dynamic determin­istic systems. The ensuing mental realignement forces the engineer and physicist to depart from a deterministic outlook which is implanted on present day engi­neering education and direct his attention to a study of complex problems such as those of turbulence and combustion based on a novel computer-based philosophy which relies on highly parallelised systems with their novel algorithmic tools. We believe that the present book "An Exploration of Chaos" will serve as a helpful in­troduction to the subject of modern dynamics and prove an incentive to dedicated young students and more experienced practitioners towards an intensification of their efforts in the eternal search and exploration of the unknown, more often than not associated with chaotic manifestations. All the aforementioned developments in the ICA reflect some of the features of the scientific revolution that has taken place in the last forty to fifty years.

Such intensity of work and dedication to research cannot be generated by a single person, but only by a team. Indeed, writing such a textbook on chaotic manifes­tations with all its intricate ramifications and the great complexities of scientific argument which have to be supported by a great number of complex figures and illustrations demands the integrated effort of a dedicated team. To comprehend such a climate and a multi-talented congregation of scientific individualists, one must oneself have experienced the severe labour of writing a textbook on an in­tellectually demanding subject which is itself undergoing such a stormy evolution. Not only knowledge is demanded, but also instinct and apprehension of future and as yet unknown evolutions.

The present Volume VII on Chaos is part of a series of treatises in English on com­puter mechanics. The previously published book on the Dynamics of Structures forms Volume V of the series. To compose the present book, the authors worked for more than six years and undertook, with student support, many studies on the topic. The present text does not reflect even a vague similarity with the first draft; it is the result of many modifications, improvements and transformations in a series of all too numerous drafts. Part of the material has been presented in a number of international lectures on the subject since 1987.

The authors subjected to these multifarious tasks were happy to call upon the support of many talents and enthusiastic experts. In the following paragraph, we would like to stress the signal significance of two intellectual stalwarts in the art of writing and bibliographic presentation.

The great creative effort required in the composition of this book could not have been realised without the splendid support of Karl Straub who instantaneously de­tected deficiencies in the presentation and contributed greatly to the high standard of the final text and figures. The second is Steffen Kernstock, who decided with the support of the senior author to expand greatly on the type-software system T^X and to construe a more sophisticated KtTgX for a professional reproduction of advanced textbooks containing a significant mathematical presentation and fig­ures which have to be entered electronically into the text. This is now history for black and white figures, but should also be realised for colour plates and figures if the necessary financial funding were secured.

Characteristic of this new technique is a dramatic difference in the pricing of sci­entific textbooks. In the case of Volume V, for example, the price of the paperback edition was reduced to a third. Possibly more significant is the fact that the final text - without any subsequent proof-reading - is produced completely within the institute of the authors. Following the completion of the text and its delivery to the publishers, we believe that the appearance of the book on the market is secured within two months. In fact, apart from the printing, only the binding process and of course the distribution remain.

To achieve these high aims, we constituted, as in our preceding publishing expe­riences, a special task force under the overall responsibility of Karl Straub and the special responsibility of Steffen Kernstock, the creator of KlTj?X. This team, an able array of multi-talented forces, included Thomas Busch, Christiane Kern­stock, Paul Sylvester Kernstock, Hans-Peter Klatt, Rolf Krentz, Petra Linhardt, Christiane Reisert, Tobias Schafer and Mahmut Tiirker. These enthusiasts were ably guided by the meticulous sense of symmetry and aesthetics of Karl Straub and Steffen Kernstock's profound knowledge and organisational skill towards the success of this venture; almost 800 megabytes of text and image data from the most varying sources and computer systems had to be combined to produce one book. We trust that the present product will satisfy even critical experts on the printing of scientific texts.

The difficult task of typing the complex text was executed with the usual perfection by Vlasta Reber-Hangi. We thank her for her dedication to work.

As mentioned before, the figures are a conditio sine qua non for the legibility and comprehensibility of a scientific text intended for graduate physicists and engineers. The aforementioned team worked with unflinching intensity towards the completion of many hundreds of figures. Their artistic sensibility and inspiration overcame all difficulties in this difficult task. A large number of the figures and all the colour plates were originally created with great precision and aesthetic sense by our former colleagues Bernd Lehle, Harald Volz and Werner Wisniewski.

We should also mention the help of Marion Hackenberg in securing all the many hundreds of references required as background reading for the composition of the text. Finally, we would like to stress that all efforts would have been in vain, had it not been for the inspired support of Marlies Parsons who, in good and bad days, stuck to her duty with Swiss clockwork precision and prepared the ground for this major bibliographic effort.

As the senior author writes these last few lines of the Preface and completes in this way the scientific text of the Volume VII, he could not help recollecting some thoughts that crossed his mind when finalising the text of Volume V of this series. It is occasionally useful not to suppress depressive ideas and to express darker feelings as well. In this mood, we consider it appropriate to stress that every coin has its two sides. In the preface, we reviewed the evolution of the ISD to the ICA and onwards to a shrinking team. The spirit of our message was. however, positivesince the success of our efforts towards a computer-oriented theory is evident. But, as we implied before, this is only one of the two sides of the coin which we view with some satisfaction. The other side is regrettably darker and involves our failure to achieve a similar level of success on the experimental side, as was realised with commendable elegance at Imperial College where the team performed brilliant experiments over many years. This discrepancy is, however, an unpredictable part of human nature and cannot be removed by a prayer. To our regret, we have to accept that talents are rare. They emerged richly in the theoretical efforts, but were only vaguely represented in the experiment. In this way, we received a damper which helps in keeping our sense of proportion. Whatever the disappointments, we hope that the positive side of the coin will prove an incentive to the reader.