The topology of chaos: Alice in stretch and squeezeland

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...

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Detalles Bibliográficos
Autores principales: Gilmore, Robert, Lefranc, Marc
Lenguaje:eng
Publicado: Wiley 2002
Materias:
Mathematical Physics and Mathematics
Acceso en línea:http://cds.cern.ch/record/611589
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author Gilmore, Robert
Lefranc, Marc
author_facet Gilmore, Robert
Lefranc, Marc
author_sort Gilmore, Robert
collection CERN
description 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
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spelling cern-6115892021-04-22T02:39:42Zhttp://cds.cern.ch/record/611589engGilmore, RobertLefranc, MarcThe topology of chaos: Alice in stretch and squeezelandMathematical Physics and MathematicsA 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 questionA 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.Wileyoai:cds.cern.ch:6115892002
spellingShingle Mathematical Physics and Mathematics
Gilmore, Robert
Lefranc, Marc
The topology of chaos: Alice in stretch and squeezeland
title The topology of chaos: Alice in stretch and squeezeland
title_full The topology of chaos: Alice in stretch and squeezeland
title_fullStr The topology of chaos: Alice in stretch and squeezeland
title_full_unstemmed The topology of chaos: Alice in stretch and squeezeland
title_short The topology of chaos: Alice in stretch and squeezeland
title_sort topology of chaos: alice in stretch and squeezeland
topic Mathematical Physics and Mathematics
url http://cds.cern.ch/record/611589
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AT lefrancmarc thetopologyofchaosaliceinstretchandsqueezeland
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AT lefrancmarc topologyofchaosaliceinstretchandsqueezeland

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