Chaos: The Science of Predictable Random Motion

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Richard Kautz (Formerly of the National Institute of Standards and Technology, Boulder, USA)

Chaos

The Science of Predictable Random Motion

Richard Kautz (Formerly of the National Institute of Standards and Technology, Boulder, USA)

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English

Oxford University Press
04 November 2010

Mathematics & Sciences; Applied mathematics; Non-linear science; Chaos theory; Dynamics & statics; Statistical physics

Based on only elementary mathematics, this engaging account of chaos theory bridges the gap between introductions for the layman and college-level texts. It develops the science of dynamics in terms of small time steps, describes the phenomenon of chaos through simple examples, and concludes with a close look at a homoclinic tangle, the mathematical monster at the heart of chaos. The presentation is enhanced by many figures, animations of chaotic motion (available on a companion CD), and biographical sketches of the pioneers of dynamics and chaos theory. To ensure accessibility to motivated high school students, care has been taken to explain advanced mathematical concepts simply, including exponentials and logarithms, probability, correlation, frequency analysis, fractals, and transfinite numbers. These tools help to resolve the intriguing paradox of motion that is predictable and yet random, while the final chapter explores the various ways chaos theory has been put to practical use.

By: Richard Kautz (Formerly of the National Institute of Standards and Technology Boulder USA)
Imprint: Oxford University Press
Country of Publication: United Kingdom
Dimensions: Height: 247mm, Width: 190mm, Spine: 20mm
Weight: 858g
ISBN: 9780199594580
ISBN 10: 0199594589
Pages: 384
Publication Date: 04 November 2010
Audience: General/trade , Young adult , ELT Advanced , Preschool (0-5)
Format: Paperback
Publisher's Status: Active

1: Chaos Everywhere 2: Galileo Galilei --- Birth of a New Science 3: Isaac Newton --- Dynamics Perfected 4: Celestial Mechanics --- Clockwork Universe 5: Pendulum --- Linear and Nonlinear 6: Josephson Effect --- Synchronization 7: Chaos Forgets the Past 8: Chaos Takes a Random Walk 9: Chaos Makes Noise 10: Edward Lorenz --- Butterfly Effect 11: Chaos Comes of Age 12: Tilt-A-Whirl --- Chaos at the Amusement Park 13: Billiard-Ball Chaos --- Atomic Disorder 14: Iterated Maps --- Chaos Made Simple 15: State Space --- Going with the Flow 16: Strange Attractor 17: Fractal Geometry 18: Stephen Smale --- Horseshoe Map 19: Henri Poincaré --- Topological Tangle 20: Chaos Goes to Work

Reviews for Chaos: The Science of Predictable Random Motion

`This is altogether a brilliantly written book that reflects the huge dedication and passion of the author to explaining the phenomenon of chaos. I can highly recommend this work to any reader who wishes to understand fundamental concepts and ideas of chaos without the need to employ any advanced mathematical formalism.' Rainer Klages, Journal of Statistical Physics `Dr. Kautz has written a book that captures the essentials of chaos in a quantitative way but without advanced mathematics. It is highly recommended for students and others with a good background in algebra and trigonometry and with a desire for a better understanding of the concepts of chaos.' Julien Clinton Sprott, University of Wisconsin - Madison `The writing style is engaging and readable... while there is a great deal of mathematical detail in the book, it is introduced carefully and thoroughly. Having a 'Dynamics Lab' of computational examples is an excellent notion, and will complement the book ideally.' Rob Sturman, University of Leeds `Kautz's Chaos provides a lively and clear introduction to many aspects of nonlinear dynamics, weaving together tales about the pendulum, Josephson junctions, the quincunx, the first four notes of Beethoven's 5th Symphony, the tilt-a-whirl and homoclinic tangles, using just algebra, geometry and trigonometry.' Robert Hilborn, University of Texas at Dallas `[Chaos] could serve as the basis for a college-level general science course as well as a resource for curious nonscientists. Kautz writes well, provides easy-to-follow explanations, and includes historical context through biographical sketches.' Eric Kincanon, Choice Reviews `Richard Kautz has written an excellent text that is suitable for undergraduates and provides the mathematical detail necessary to give a thorough introduction to chaos ... a superb book that presents chaos and chaotic systems so that readers will understand the concepts and understand what is so fascinating about this phenomenon ... I highly recommend this book.' David Mazel, MAA Reviews