The Topology of Chaos
Alice in Stretch and Squeeze Land
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Topology of Chaos by Robert Gilmore
Book DescriptionA new approach to understanding nonlinear dynamics and strange attractors The behavior of a physical system may appear irregular or chaotic even when it is completely deterministic and predictable for short periods of time into the future. How does one model the dynamics of a system operating in a chaotic regime? Older tools such as estimates of the spectrum of Lyapunov exponents and estimates of the spectrum of fractal dimensions do not sufficiently answer this question. In a significant evolution of the field of Nonlinear Dynamics, The Topology of Chaos responds to the fundamental challenge of chaotic systems by introducing a new analysis method-Topological Analysis-which can be used to extract, from chaotic data, the topological signatures that determine the stretching and squeezing mechanisms which act on flows in phase space and are responsible for generating chaotic data. Beginning with an example of a laser that has been operated under conditions in which it behaved chaotically, the authors convey the methodology of Topological Analysis through detailed chapters on: Discrete Dynamical Systems: Maps Continuous Dynamical Systems: Flows Topological Invariants Branched Manifolds The Topological Analysis Program Fold Mechanisms Tearing Mechanisms Unfoldings Symmetry Flows in Higher Dimensions A Program for Dynamical Systems Theory Suitable at the present time for analyzing "strange attractors" that can be embedded in three-dimensional spaces, this groundbreaking approach offers researchers and practitioners in the discipline a complete and satisfying resolution to the fundamental questions of chaotic systems.
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Book DetailsISBN: 9780471408161
(249mm x 180mm x 36mm)
Imprint: John Wiley & Sons Inc
Publisher: John Wiley and Sons Ltd
Publish Date: 11-Oct-2002
Country of Publication: United States
Books By Author Robert Gilmore
Topology of Chaos, Hardback (November 2011)
Innovative methods for the analysis of chaotic systems, in this second edition completed by a broad introduction for the non expert, additional chapters on embeddings, bounding tori, and the representation theory for strange attractors, and frequently asked questions.
Lie Groups, Physics, and Geometry, Hardback (January 2008)
Introduction to Lie groups for graduate and undergraduate students in physics, mathematics and electrical engineering.
Symmetry of Chaos, Hardback (January 2007)» View all books by Robert Gilmore
Why have scientists, engineers, and mathematicians become intrigued by chaos? Chaos is about predictability in even the most unstable systems, and symmetry is a pattern of predictability - a conceptual tool to help understand complex behaviour. This book aims to treat this interplay between chaos and symmetry.
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Author Biography - Robert Gilmore
ROBERT GILMORE, PhD, is a professor in the Physics Department of Drexel University, Philadelphia, Pennsylvania. MARC LEFRANC, PhD, is a researcher at the Centre National de la Recherche Scientifique in the Laboratoire de Physique des Lasers, Atomes, Molecules at the Universite des Sciences et Technologies de Lille, France.
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