This book, the first in the Cambridge Nonlinear Science Series, presents the fundamentals of chaos theory in conservative systems, providing a systematic study of the theory of transitional states of physical systems which lie between deterministic and chaotic behaviour. The authors' treatment of transitions to chaos, the theory of stochastic layers and webs, and the numerous applications of this theory, particularly to pattern symmetry, will make the book of importance to scientists from many disciplines.The authors have been meticulous in providing a detailed presentation of the material, enabling the reader to learn the necessary computational methods and to apply them in other problems. The inclusion of a significant amount of computer graphics is also an important aid to understanding. The final section of the book contains a fascinating collection of patterns in art and living nature. The book will be of interest to graduate students and researchers in physics and mathematics who are interested in problems of chaos, irreversibility, statistical mechanics and theories of spatial patterns and symmetries. The perhaps unconventional links between chaos theory and other topics make the book particularly interesting.

This 1989 book is about chaos, fractals and complex dynamics, and is addressed to all people who have some familiarity with computers and enjoy using them. The mathematics has been kept simple, with few formulae, yet the reader is introduced to and can learn about an area of current scientific research which was scarcely possible before the availability of computers. The introduction is achieved through the extensive use of computer graphics. The book is divided into two main parts: in the first the most interesting problems are described, with, in each case, a solution in the form of a computer program. A large number of exercises enable the reader to undertake his or her own experimental work. In the second part, example programs are given for specific machines and operating systems; details refer to MS-DOC and Turbo-Pascal, UNIX 4.2 BSD with Berkley Pascal and C. Other implementations of the graphics routines are given for Apple Macintosh, Apple IIE and IIGS and Atari ST.

This 1989 book is about chaos, fractals and complex dynamics, and is addressed to all people who have some familiarity with computers and enjoy using them. The mathematics has been kept simple, with few formulae, yet the reader is introduced to and can learn about an area of current scientific research which was scarcely possible before the availability of computers. The introduction is achieved through the extensive use of computer graphics. The book is divided into two main parts: in the first the most interesting problems are described, with, in each case, a solution in the form of a computer program. A large number of exercises enable the reader to undertake his or her own experimental work. In the second part, example programs are given for specific machines and operating systems; details refer to MS-DOC and Turbo-Pascal, UNIX 4.2 BSD with Berkley Pascal and C. Other implementations of the graphics routines are given for Apple Macintosh, Apple IIE and IIGS and Atari ST.

An accessible account of systems that display a chaotic time evolution, which although determinative, reveals features more characteristic of a statistical technique known as time series analysis.

This book presents leading-edge research on artificial life, cellular automata, chaos theory, cognition, complexity theory, synchronisation, fractals, genetic algorithms, information systems, metaphors, neural networks, non-linear dynamics, parallel computation and synergetics. The unifying feature of this research is the tie to chaos and complexity.

Part of the Princeton Aeronautical Paperback series designed to bring to students and research engineers outstanding portions of the twelve-volume High Speed Aerodynamics and Jet Propulsion series. These books have been prepared by direct reproduction of the text from the original series and no attempt has been made to provide introductory material or to eliminate cross reference to other portions of the original volumes. Originally published in 1960. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

From its original meaning as a gaping void, or the emptiness that precedes the whole of creation, chaos has taken on the exclusive meaning of confusion, pandemonium and mayhem. This definition has become the overarching word to describe any challenge to the established order; be it railway strikes or political dissent, any unexpected event is routinely described in the media and popular parlance as 'chaos'. In his incisive new study, Stuart Walton argues that this is a pitifully one-dimensional view of the world, as he looks to many of the great social, political, artistic and philosophical advances that have emerged from periods of disorder and from the refusal to think within the standard paradigms. Exploring this worldview, Walton contends that we are superstitious about states of affairs in which anything could happen because we have been taught to prefer the imposition of rules in every aspect of our lives, from our diets to our romances. Indeed, in An Excursion through Chaos he demonstrates how it is these very restrictions that are responsible for the alienation that has characterised postwar society, a state of disengagement that could have been avoided if we had taken a less fearful attitude towards the unravelling of order.

Almost every scientist has heard of catastrophe theory and knows that there has been a considerable amount of controversy surrounding it. Yet comparatively few know anything more about it than they may have read in an article written for the general public. The aim of this book is to make it possible for anyone with a comparatively modest background in mathematics - no more than is usually included in a first year university course for students not specialising in the subject - to understand the theory well enough to follow the arguments in papers in which it is used and, if the occasion arises, to use it. Over half the book is devoted to applications, partly because it is not possible yet for the mathematician applying catastrophe theory to separate the analysis from the original problem. Most of these examples are drawn from the biological sciences, partly because they are more easily understandable and partly because they give a better illustration of the distinctive nature of catastrophe theory. This controversial and intriguing book will find applications as a text and guide to theoretical biologists, and scientists generally who wish to learn more of a novel theory.

Almost every scientist has heard of catastrophe theory and knows that there has been a considerable amount of controversy surrounding it. Yet comparatively few know anything more about it than they may have read in an article written for the general public. The aim of this book is to make it possible for anyone with a comparatively modest background in mathematics - no more than is usually included in a first year university course for students not specialising in the subject - to understand the theory well enough to follow the arguments in papers in which it is used and, if the occasion arises, to use it. Over half the book is devoted to applications, partly because it is not possible yet for the mathematician applying catastrophe theory to separate the analysis from the original problem. Most of these examples are drawn from the biological sciences, partly because they are more easily understandable and partly because they give a better illustration of the distinctive nature of catastrophe theory. This controversial and intriguing book will find applications as a text and guide to theoretical biologists, and scientists generally who wish to learn more of a novel theory.

The editors (of the Universite et Institut National des Sciences Appliquees de Rouen, France) present six chapters exploring the application of chaos theory to such topics as the topological characterisation of attractors and the reconstruction of equations of motion from data. Specific topics include the development of a method of modelling called NARMAX (non-linear autoregressive moving average models with exogenous outputs), a summary of the work of the Centre of Applied Dynamics and Optimisation at the U. of Western Australia), time delayed feedback systems, and global modelling applications to biological data and secure communication.

This volume sets out the basic applied mathematical and numerical methods of chaotic dynamics and illustrates the wide range of phenomena, inside and outside the laboratory, that can be treated as chaotic processes.

Originally published in 1986.

The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These paperback editions preserve the original texts of these important books while presenting them in durable paperback editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Covering one of the fastest growing areas of applied mathematics, Nonlinear Dynamics and Chaos: Second Edition, is a fully updated edition of this highly respected text. Covering a breadth of topics, ranging from the basic concepts to applications in the physical sciences, the book is highly illustrated and written in a clear and comprehensible style.

• Provides a self-contained introduction to the theory and applications of nonlinear dynamics and chaos.

• Introduces the concepts of instabilities, bifurcations, and catastrophes.

• Each idea is carefully explained and supported by examples.

• Features many applications to a wide variety of scientific fields.

• Includes an illustrated glossary of geometrical dynamics.

• Features a supplementary bibliography of further reading.

• Assumes minimal background knowledge.

Mathematical symmetry and chaos come together to form striking, beautiful colour images throughout this impressive work, which addresses how the dynamics of complexity can produce familiar universal patterns. The book, a richly illustrated blend of mathematics and art, was widely hailed in publications as diverse as the New York Review of Books, Scientific American, and Science when first published in 1992. This much-anticipated second edition features many new illustrations and addresses the progress made in the mathematics and science underlying symmetric chaos in recent years; for example, the classifications of attractor symmetries and methods for determining the symmetries of higher dimensional analogues of images in the book. In particular, the concept of patterns on average and their occurrence in the Faraday fluid dynamics experiment is described in a revised introductory chapter. The ideas addressed in this book have been featured at various conferences on intersections between art and mathematics, including the annual Bridges conference, and in lectures to art students at the University of Houston.

In this volume are collected notes of lectures delivered at the First In ternational Research Institute of the Mathematical Society of Japan. This conference, held at Tohoku University in July 1993, was devoted to geometry and global analysis. Subsequent to the conference, in answer to popular de mand from the participants, it was decided to publish the notes of the survey lectures. Written by the lecturers themselves, all experts in their respective fields, these notes are here presented in a single volume. It is hoped that they will provide a vivid account of the current research, from the introduc tory level up to and including the most recent results, and will indicate the direction to be taken by future researeh. This compilation begins with Jean-Pierre Bourguignon's notes entitled "An Introduction to Geometric Variational Problems," illustrating the gen eral framework of the field with many examples and providing the reader with a broad view of the current research. Following this, Kenji Fukaya's notes on "Geometry of Gauge Fields" are concerned with gauge theory and its applications to low-dimensional topology, without delving too deeply into technical detail. Special emphasis is placed on explaining the ideas of infi nite dimensional geometry that, in the literature, are often hidden behind rigorous formulations or technical arguments."

Part of the Princeton Aeronautical Paperback series designed to bring to students and research engineers outstanding portions of the twelve-volume High Speed Aerodynamics and Jet Propulsion series. These books have been prepared by direct reproduction of the text from the original series and no attempt has been made to provide introductory material or to eliminate cross reference to other portions of the original volumes. Originally published in 1960. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

This volume sets out the basic applied mathematical and numerical methods of chaotic dynamics and illustrates the wide range of phenomena, inside and outside the laboratory, that can be treated as chaotic processes. Originally published in 1986. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

This book is the the English Language Version of the very successful German textbook, "Modellbildung und Simulation." It provides a self-contained and complete guide to the methods and mathematical background of modeling and simulation software of dynamic systems. Furthermore, an appropriate simulation software and a collection of dynamic system models (on the accompanying disk) are highlights of the book/software-Package.Dies ist die englischsprachige Ausgabe des sehr erfolgreichen Lehrbuches "Modellbildung und Simulation." Geboten wird eine vollstandige Einfuhrung in die Methoden der Simulation dynamischer Systeme, wobei auch der notwendige mathematische Hintergrund vermittelt wird. Ausserdem ist eine Simulationssoftware Bestandteil des Werkes; auf der beiliegenden Diskette befinden sich ferner 50 Beispielsysteme ("Systemzoo"), die zur spielerischen Einubung der verwendeten Verfahren hilfreich sind."

Komplexe dynamische Systeme werden in verschiedenen Wissenschaftsdisziplinen untersucht - von Physik, Chemie, Biologie und Medizin uber Kognitionswissenschaften und Psychologie bis zu Soziologie und OEkonomie. Dieser Band zieht Bilanz und zeigt kunftige Forschungsperspektiven auf. Gemeinsames methodisches Thema ist die Modellierung komplexer Systeme, deren Dynamik durch Nichtlinearitat bestimmt ist. Mathematische Methoden und Computersimulationen machen aber nur Sinn, wenn sie mit konkreten einzelwissenschaftlichen Analysen verbunden sind. Das Buch liefert nicht nur fachubergreifende Informationen uber den aktuellen Forschungsstand, sondern kann auch von Nichtspezialisten als Einfuhrung in das spannende Gebiet komplexer Systeme und nichtlinearer Dynamik in Natur und Gesellschaft gelesen werden.

This text presents concepts on chaos in discrete time dynamics that are accessible to anyone who has taken a first course in undergraduate calculus. Retaining its commitment to mathematical integrity, the book, originating in a popular one-semester middle level undergraduate course, constitutes the first elementary presentation of a traditionally advanced subject.

In a totally new way of looking at financial economics, Nonlinear Pricing abandons the traditional assumptions of equilibrium in economics and randomness in a time-series. These shortcomings are becoming increasingly awkward given a superior technological infrastructure and advances in mathematics and the sciences. Despite these advances and their empirical proof, much remains confused or muddled. In this groundbreaking new book, leading hedge fund manager Christopher T. May explores the nature and role of nonlinearity, an inherent part of everyday reality, and illustrates a profit-making strategy.

One of the many striking applications of nonlinear technology in recent years, nonlinear pricing uses cutting-edge technology to identify and exploit patterns hidden within the seemingly helter-skelter rise and fall of daily stock prices. Nonlinear Pricing sheds much needed light on the principles behind this innovative view of reality and provides clear explanations of how it is employed to predict—at least partially—the unpredictable.

Beginning with an incisive introduction to the topic, May presents the roots of nonlinearity through the examples of calendrics, geometry, and music. He then illustrates the application and integration of various nonlinear technologies, including genetic algorithms, fuzzy logic, fractal imaging, and nonlinear dynamics, to such essentials as trading strategies, asset allocation, risk management, and derivative pricing and hedging. Along with practical methodologies and a wealth of real-world examples, this comprehensive resource contains a glossary of terms, a bibliography, and in-depth information on:

• Fractal analysis—power law distributions, fractional Brownian motion, and their relationships
• The Hurst Exponent—the KAOS screen and its practical implementation
• Resonance—time domain versus frequency domain, Brownian motion, and the Gaussian distribution
• Advanced concepts—Soros's Reflexivity, nonequilibrium economics, kernel of theoretical nonlinear pricing, May's Law, resolution and resonance.

"Nonlinear Pricing is an eminently readable book which I found satisfied both the theorist and the practitioner in me. For the theorist, there are new insights into the relationship between complexity and the markets. For the practitioner, there are practical ideas on how to fashion investment strategies. I highly recommend Nonlinear Pricing to all students of the markets."—Edgar E. Peters, Chief Investment Strategist, PanAgora Asset Management; author, Chaos and Order in the Capital Markets.

"Nonlinear Pricing goes further than any book I am aware of in drawing a connection between the real world of economics and the new ideas about economics coming from the science of self-organized systems. Written in a lively, informal style, this is a wonderful read for those of us who have been wondering whether anyone understands anything at all about how markets work."—Lee Smolin, PhD, Department of Physics, Pennsylvania State University.

"Required reading for the enlightened financial professional. Enjoyable for the intelligent investor. A dash of physics, bite-sized pieces of nonlinear concepts, and a broth of hands-on experience make this a cookbook for the modern trader."—Richard E. Morley, Potts Medal recipient and founder of the Breakfast Club.

"A real eye-opener—Nonlinear Pricing explains a complex subject in easy terms and makes the reader aware of the many opportunities offered by this new technology."—Richard Olsen, founder, Olsen and Associates, Zurich.

"I, of course, think highly of this book as it credits Dance of the Money Bees with inventing 'swarm theory,' now a discipline in computer science. There are many other splendid insights."—John Train, author and President of the Montrose Fund

"An extraordinary tour d'horizon, this book challenges conventional thinking about finance, investing, and much else besides. Brimming with ideas and eye-opening connections, it makes a powerful case for our need to understand the extent to which nonlinearity shapes our lives."—Andrew Freeman, Managing Editor, Financial Services, The Economist Intelligence Unit; coauthor, Seeing Tomorrow: Rewriting the Rules of Risk.

"Nonlinear Pricing: Theory & Applications by Christopher T. May makes nice reading even for people like me who are not economists. This is an ambitious book as it presents economics starting from fundamental physics. It deserves a large readership."—Ilya Prigogine, 1977 Nobel Laureate, Chemistry; author, The End of Certainty; and world's foremost non-equilibrium scientist.

Written by one of the few practitioners using this breakthrough methodology to trade the markets successfully, Nonlinear Pricing fills an important niche in investment literature. It is a must read for anyone seeking to understand—and capitalize on—twenty-first century financial economics.

Das Buch wendet sich an Leser, die - uber die rein computergraphische Darstellung hinaus - an einer analytischen Untersuchung von chaotischen und nichtchaotischen Differenzen- und Differentialgleichungssystemen interessiert sind. Breiter Raum wird der Durchrechnung von Beispielen gegeben. Dargestellt werden zunachst qualitative Methoden als auch solche, die das Auffinden von Attraktoren, Bifurkationen etc. und deren Klassifikation in Abhangigkeit von den Systemparametern gestatten. Der letzte Teil schliesslich widmet sich der quantitativen Beschreibung chaotischer Systeme. Dazu werden zuerst die Begriffe Chaos und Fraktal exakt definiert und dann die verschiedenen fraktalen Dimensionen, Lyapunov-Exponenten, Entropien etc. eingefuhrt und durch Beispiele begrundet."