The Topology of Chaos

Robert Gilmore, Marc Lefranc

496 pages, parution le 29/10/2002

Ajouter à une liste

Indisponible

Résumé

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.
Contents

1. Introduction.
2. Discrete 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

L'auteur - Robert Gilmore

Robert Gilmore enseigne la physique à l'Université de Bristol, en Grande-Bretagne. Au cours de sa longue carrière, il a travaillé au laboratoire National de Brookhaven, au Laboratoire de l'Accélérateur Linéaire de Stanford, aux Etats-Unis, et au Centre Européen de Recherches Nucléaires (CERN) à Genève. Il est l'auteur de plusieurs livres de vulgarisation à grand succès comme Alice au pays des quanta (Le Pommier, 2000)

Caractéristiques techniques

	PAPIER
Éditeur(s)	Wiley
Auteur(s)	Robert Gilmore, Marc Lefranc
Parution	29/10/2002
Nb. de pages	496
Format	16 x 24
Couverture	Relié
Poids	860g
Intérieur	Noir et Blanc
EAN13	9780471408161
ISBN13	978-0-471-40816-1