The topology of chaos : Alice in stretch and squeezeland / / Robert Gilmore and Marc Lefranc

• Record Nr.: UNINA9910130960403321
• Autore: Gilmore Robert
• Pubbl/distr/stampa: Weinheim, Germany : , : WILEY-VCH Verlag GmbH & Co. KGaA, , 2011; ©2011
• ISBN: 3-527-63942-X; 3-527-63941-1; 3-527-63940-3
• Edizione: [2nd ed.]
• Descrizione fisica: 1 online resource (1129 p.)
• Disciplina: 003.857; 514.74; 514/.74
• Soggetti: Chaotic behavior in systems
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: Cover; Half Title page; Related Titles; Title page; Copyright page; Preface to Second Edition; Preface to the First Edition; Chapter 1: Introduction; 1.1 Brief Review of Useful Concepts; 1.2 Laser with Modulated Losses; 1.3 Objectives of a New Analysis Procedure; 1.4 Preview of Results; 1.5 Organization of This Work; Chapter 2: Discrete Dynamical Systems: Maps; 2.1 Introduction; 2.2 Logistic Map; 2.3 Bifurcation Diagrams; 2.4 Elementary Bifurcations in the Logistic Map; 2.5 Map Conjugacy; 2.6 Fully Developed Chaos in the Logistic Map; 2.7 One-Dimensional Symbolic Dynamics; 2.8 Shift Dynamical Systems, Markov Partitions, and Entropy2.9 Fingerprints of Periodic Orbits and Orbit Forcing; 2.10 Two-Dimensional Dynamics: Smale's Horseshoe; 2.11 Hénon Map; 2.12 Circle Maps; 2.13 Annulus Maps; 2.14 Summary; Chapter 3: Continuous Dynamical Systems: Flows; 3.1 Definition of Dynamical Systems; 3.2 Existence and Uniqueness Theorem; 3.3 Examples of Dynamical Systems; 3.4 Change of Variables; 3.5 Fixed Points; 3.6 Periodic Orbits; 3.7 Flows Near Nonsingular Points; 3.8 Volume Expansion and Contraction; 3.9 Stretching and Squeezing; 3.10 The Fundamental Idea; ; 3.11 Summary; Chapter 4: Topological Invariants4.1 Stretching and Squeezing Mechanisms; 4.2 Linking Numbers; 4.3 Relative Rotation Rates; 4.4 Relation between Linking Numbers and Relative Rotation Rates; 4.5 Additional Uses of Topological Invariants; 4.6 Summary; Chapter 5: Branched Manifolds; 5.1 Closed Loops; 5.2 What Does This Have to Do with Dynamical Systems?; 5.3 General Properties of Branched Manifolds; 5.4 Birman-Williams Theorem; 5.5 Relaxation of Restrictions; 5.6 Examples of Branched Manifolds; 5.7 Uniqueness and Nonuniqueness; 5.8 Standard Form; 5.9 Topological Invariants; 5.10 Additional Properties5.11 Subtemplates; 5.12 Summary; Chapter 6: Topological Analysis Program; 6.1 Brief Summary of the Topological Analysis Program; 6.2 Overview of the Topological Analysis Program; 6.3 Data; 6.4 Embeddings; 6.5 Periodic Orbits; 6.6 Computation of Topological Invariants; 6.7 Identify Template; 6.8 Validate Template; 6.9 Model Dynamics; 6.10 Validate Model; 6.11 Summary; Chapter 7: Folding Mechanisms: A2; 7.1 Belousov-Zhabotinskii Chemical Reaction; 7.2 Laser with Saturable Absorber; 7.3 Stringed Instrument; 7.4 Lasers with Low-Intensity Signals; 7.5 The Lasers in Lille; 7.6 The Laser in Zaragoza7.7 Neuron with Subthreshold Oscillations; 7.8 Summary; Chapter 8: Tearing Mechanisms: A3; 8.1 Lorenz Equations; 8.2 Optically Pumped Molecular Laser; 8.3 Fluid Experiments; 8.4 Why A3?; 8.5 Summary; Chapter 9: Unfoldings; 9.1 Catastrophe Theory as a Model; 9.2 Unfolding of Branched Manifolds: Branched Manifolds as Germs; 9.3 Unfolding within Branched Manifolds: Unfolding of the Horseshoe; 9.4 Missing Orbits; 9.5 Routes to Chaos; 9.6 Orbit Forcing and Topological Entropy: Mathematical Aspects; 9.7 Topological Measures of Chaos in Experiments; 9.8 Summary; Chapter 10: Symmetry
• Sommario/riassunto: A highly valued resource for those who wish to move from the introductory and preliminary understandings and the measurement of chaotic behavior to a more sophisticated and precise understanding of chaotic systems. The authors provide a deep understanding of the structure of strange attractors, how they are classified, and how the information required to identify and classify a strange attractor can be extracted from experimental data.In its first edition, the Topology of Chaos has been a valuable resource for physicist and mathematicians interested in the topological analysis of dynamical