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.
Rezensionen / Stimmen
The book is a famous introduction into the wide field of chaos and provides a very good basis for further studies. It is very useful for ... students in engineering, natural sciences, and mathematics or people interested in a better understanding of the nature of chaos. It is highly recommended. * Bernd Platzer, Journal of Applied Mathematics and Mechanics * Kautz's [Chaos] functions at the level of Ruelle's [Chance and Chaos] but is more focused and compete. It brings a thorough and fresh approach to the task. The writing is lucid and very engaging ... and the illustrations are uniformly excellent. * James Blackburn, American Journal of Physics * 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 *
Sprache
Verlagsort
Zielgruppe
Für Jugendliche
General readers, high-school and undergraduate students, and practising scientists who want a quick and easily accessible introduction to chaos theory.
Illustrationen
168 b/w line and halftone illustrations
Maße
Höhe: 253 mm
Breite: 195 mm
Dicke: 25 mm
Gewicht
ISBN-13
978-0-19-959457-3 (9780199594573)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Klassifikation
Richard Kautz is an engineer and physicist who holds a doctorate from the Massachusetts Institute of Technology. During his career at the National Institute of Standards and Technology, he helped develop fundamental quantum standards for both voltage and capacitance. Kautz is a Fellow of the American Physical Society and a recipient of the Samuel Stratton Award for measurement science and the Edward Condon Award for scientific writing.
Autor*in
Formerly of the National Institute of Standards and Technology, Boulder, USA
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 Poincare -- Topological Tangle ; 20. Chaos Goes to Work
