The Topology of Chaos: Alice in Stretch and Squeeze Land by Robert Gilmore, Marc Lefranc (Hardback, 2002)
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- DescriptionA new approach to understanding nlinear 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 Lyapuv exponents and estimates of the spectrum of fractal dimensions do t 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.
- Author BiographyROBERT 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.
- Author(s)Marc Lefranc,Robert Gilmore
- PublisherJohn Wiley and Sons Ltd
- Date of Publication11/10/2002
- Place of PublicationNew York
- Country of PublicationUnited States
- ImprintJohn Wiley & Sons Inc
- Content Notereferences, glossary, index
- Weight1068 g
- Width180 mm
- Height249 mm
- Spine36 mm
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