The Topology of Chaos

Alice in Stretch and Squeezeland

Robert Gilmore, Marc Lefranc (Autoren)

Buch | Hardcover

518 Seiten

2002
Wiley-VCH Publishers Inc.,U.S. (Verlag)
978-0-471-40816-1 (ISBN)

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Describes how strange attractors are classified and presents the simple algorithm for extracting this information from experimental data. * There have been many books published on the first two tools for classifying strange attractors, but this is the first book on the third * Written by the originator of the method .

A 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.

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, Molécules at the Université des Sciences et Technologies de Lille, France.

Preface.

1. Introduction.

2. Dscrete Dynamical Systems: Maps.

3. Continuous Dynamical Systems: Flows.

4. Topological Invariants.

5. Branched Manifolds.

6. Topological Analysis Program.

7. Folding Mechanisms: A2.

8. Tearing Mechanisms: A3.

9. Unfoldings.

10. Symmetry.

11. Flows in Higher Dimensions.

12. Program for Dynamical Systems Theory.

Appendix A: Determining Templates from Topological Invariants.

References.

Topic Index.

Sprache	englisch
Maße	178 x 249 mm
Gewicht	1077 g
Themenwelt	Mathematik / Informatik ► Informatik ► Theorie / Studium
	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
	Naturwissenschaften ► Physik / Astronomie
ISBN-10	0-471-40816-6 / 0471408166
ISBN-13	978-0-471-40816-1 / 9780471408161
Zustand	Neuware