The Symmetry of Chaos

Hardcover | May 18, 2007

byRobert Gilmore, Christophe Letellier

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There is a tremendous fascination with chaos and fractals, about which picture books can be found on coffee tables everywhere. Chaos and fractals represent hands-on mathematics that is alive and changing. One can turn on a personal computer and create stunning mathematical images that no onehas ever seen before. Chaos and fractals are part of dynamics, a larger subject that deals with change, with systems that evolve with time. Whether the system in question settles down to equilibrium, keeps repeating in cycles, or does something more complicated, it is dynamics that scientists and mathematicians use toanalyze a system's behavior. Chaos is the term used to describe the apparently complex behavior of what we consider to be simple, well-behaved systems. Chaotic behavior, when looked at casually, looks erratic and almost random. The type of behavior that in the last 20 years has come to be calledchaotic arises in very simple systems. In fact, these systems are essentially deterministic; that is, precise knowledge of the conditions of a system allow future behavior of the system to be predicted. The problem of chaos is to reconcile these apparently conflicting notions: randomness andpredictability. Why have scientists, engineers, and mathematicians become intrigued by chaos? The answer to that question has two parts: (1) the study of chaos has provided new conceptual tools enabling scientists to categorize and understand complex behavior and (2) chaotic behavior seems to be universal - fromelectrical circuits to nerve cells. Chaos is about predictability in even the most unstable systems, and symmetry is a pattern of predictability - a conceptual tool to help understand complex behavior. The Symmetry of Chaos treats this interplay between chaos and symmetry. This graduate textbook inphysics, applied mathematics, engineering, fluid dynamics, and chemistry is full of exciting new material, illustrated by hundreds of figures. Nonlinear dynamics and chaos are relatively young fields, and in addition to serving textbook markets, there is a strong interest among researchers in newresults in the field. The authors are the foremost experts in this field, and this book should give a definitive account of this branch of dynamical systems theory.

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There is a tremendous fascination with chaos and fractals, about which picture books can be found on coffee tables everywhere. Chaos and fractals represent hands-on mathematics that is alive and changing. One can turn on a personal computer and create stunning mathematical images that no onehas ever seen before. Chaos and fractals ar...

Robert Gilmore is a Professor in the Physics Department at Drexel University. Christophe Letellier is a Chaotician at Universite de Rouen.

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Format:HardcoverDimensions:560 pages, 6.3 × 9.29 × 1.3 inPublished:May 18, 2007Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0195310659

ISBN - 13:9780195310658

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Table of Contents

Part IExamples and Simple Application1. Introduction2. Simple Symmetries3. Image Dynamical Systems4. Covers5. Peeling Bifurcations6. Three-Fold and Four-Fold covers7. Multichannel Intermittency8. Driven Two-Dimensional Dynamical Systems9. Larger SymmetriesPart IIMathematical Foundations10. Group Theory Basics11. Invariant Polynomials12. Equivariant Dynamics in R N13. Covering Dynamical Systems14. Symmetries Due to SymmetryPart IIISymmetry without Groups: Topology15. symmetry without Groups: "Topological Symmetry"16. All the Covers of the HorsehoeAppendix A A Potpourri of Equivariant SystemsReferencesIndex