Chaos and Nonlinear Dynamics: An Introduction for Scientists and Engineers

Paperback | August 15, 2000

byRobert C. Hilborn

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Chaos and Nonlinear Dynamics introduces students, scientists, and engineers to the full range of activity in the rapidly growing field on nonlinear dynamics. Using a step-by-step introduction to dynamics and geometry in state space as the central focus of understanding nonlinear dynamics, thisbook includes a thorough treatment of both differential equation models and iterated map models (including a derivation of the famous Feigenbaum numbers). It is the only book at this level to include the increasingly important field of pattern formation and a survey of the controversial questions ofquantum chaos. Important tools such as Lyapunov exponents and fractal dimensions are treated in detail. With over 200 figures and diagrams, and analytic and computer exercises for every chapter, the book can be used as a course-text or for self-instruction. This second edition has been restructuredto make the book even more useful as a course text:many of the more complex examples and derivations have been moved to appendices. The extensive collection of annotated references has been updated through January 2000 and now includes listings of World Wide Web sites at many of the major nonlineardynamics research centers. From reviews on the 1/e: 'What has been lacking is a single book that takes the reader with nothing but a knowledge of elementary calculus and physics all the way to the frontiers of research in chaos and nonlinear dynamics in all its facets. [...] a serious student,teacher, or researcher would be delighted to have this book on the shelf as a reference and as a window to the literature in this exciting and rapidly growing new field of chaos.' J.C. Sprott, American Journal of Physics, September 19944 'I congratulate the author on having managed to write anextremely thorough, comprehensive, and entertaining introduction to the fascinating field of nonlinear dynamics. His book is highly self- explanatory and ideally suited for self-instruction. There is hardly any question that the author does not address in an exceptionally readable manner. [...] Istrongly recommend it to those looking for a comprehensive, practical, and not highly mathematical approach to the subject.' E.A. Hunt, IEEE Spectrum, December 1994

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From the Publisher

Chaos and Nonlinear Dynamics introduces students, scientists, and engineers to the full range of activity in the rapidly growing field on nonlinear dynamics. Using a step-by-step introduction to dynamics and geometry in state space as the central focus of understanding nonlinear dynamics, thisbook includes a thorough treatment of both ...

Robert C. Hilborn, Department of Physics and Astronomy, University of Nebraska-Lincoln
Format:PaperbackPublished:August 15, 2000Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0198507232

ISBN - 13:9780198507239

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Table of Contents

First Edition PrefaceFirst Edition AcknowledgmentsSecond Edition PrefaceSecond Edition AcknowledgmentsI. The Phenomenology of Chaos1. Three Chaotic Systems2. The Universality of ChaosII. Towards a Theory of Nonlinear Dynamics and Chaos3. Dynamics in State Space: One and Two Dimensions4. Three-Dimensional State Space and Chaos5. Iterated Maps6. Quasi-Periodicity and Chaos7. Intermittency and Crises8. Hamiltonian SystemsIII.Measures of Chaos9. Quantifying Chaos10. Many Dimensions and MultifractalsIV.Special Topics11. Pattern Formation and Spatiotemporal Chaos12. Quantum Chaos, The Theory of Complexity, and other TopicsAppendix A: Fourier Power SpectraAppendix B: Bifurcation TheoryAppendix C: The Lorenz ModelAppendix D: The Research Literature on ChaosAppendix E: Computer ProgramsAppendix F: Theory of the Universal Feigenbaum NumbersAppendix G: The Duffing Double-Well OscillatorAppendix H: Other Universal Feature for One-Dimensional Iterated MapsAppendix I: The van der Pol OscillatorAppendix J: Simple Laser Dynamics ModelsReferencesBibliographyIndex

Editorial Reviews

"It was a pleasure to read and I am enthusiastically looking forward to seeing its third edition."--Nonlinear Dynamics