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Topology and dynamics of chaos : in celebration of Robert Gilmore's 70th birthday

Author: Christophe Letellier; Robert Gilmore; World Scientific (Firm)
Publisher: Singapore ; Hackensack, N.J. : World Scientific Pub. Co., ©2013.
Series: World Scientific series on nonliear science., Series A,, Monographs and treatises ;, v. 84.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
The book surveys how chaotic behaviors can be described with topological tools and how this approach occurred in chaos theory. Some modern applications are included. The contents are mainly devoted to topology, the main field of Robert Gilmore's works in dynamical systems. They include a review on the topological analysis of chaotic dynamics, works done in the past as well as the very latest issues. Most of the  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Christophe Letellier; Robert Gilmore; World Scientific (Firm)
ISBN: 9789814434867 9814434868
OCLC Number: 844310930
Description: 1 online resource (x, 351 pages) : illustrations (some color), color map, portraits.
Contents: 1. Introduction to topological analysis / Christophe Letellier & Robert Gilmore --
2. The peregrinations of Poincare / R. Abraham --
3. A Toulouse research group in the "prehistoric" times of chaotic dynamics / Christian Mira --
4. Can we trust in numerical computations of chaotic solutions of dynamical systems? / Rene Lozi --
5. Chaos hierarchy --
a review, thirty years later / Otto E. Rossler & Christophe Letellier --
6. The mathematics of Lorenz knots / Joan S. Birman --
7. A braided view of a knotty story / Mario Natiello & Hernan Solari --
8. How topology came to chaos / Robert Gilmore --
9. Reflections from the fourth dimension / Marc Lefranc --
10. The symmetry of chaos / Christophe Letellier --
11. The shape of ocean color / Nicholas Tufillaro --
12. Low dimensional dynamics in biological motor patterns / Gabriel B. Mindlin --
13. Minimal smooth chaotic flows / Jean-Marc Malasoma --
14. The chaotic marriage of physics and financial economics / Claire Gilmore --
15. Introduction of the sphere map with application to spin-torque nano-oscillators / Keith Gilmore & Robert Gilmore --
16. Robert Gilmore, a portrait / Hernan G. Solari.
Series Title: World Scientific series on nonliear science., Series A,, Monographs and treatises ;, v. 84.
Responsibility: edited by Christophe Letellier, Robert Gilmore.

Abstract:

The book surveys how chaotic behaviors can be described with topological tools and how this approach occurred in chaos theory. Some modern applications are included. The contents are mainly devoted to topology, the main field of Robert Gilmore's works in dynamical systems. They include a review on the topological analysis of chaotic dynamics, works done in the past as well as the very latest issues. Most of the contributors who published during the 90's, including the very well-known scientists Otto Rossler, Rene Lozi and Joan Birman, have made a significant impact on chaos theory, discrete chaos, and knot theory, respectively. Very few books cover the topological approach for investigating nonlinear dynamical systems. The present book will provide not only some historical - not necessarily widely known - contributions (about the different types of chaos introduced by Rossler and not just the "Rossler attractor "; Gumowski and Mira's contributions in electronics; Poincare's heritage in nonlinear dynamics) but also some recent applications in laser dynamics, biology, etc.

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