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Order and Chaos in Nonlinear Physical Systems

  • Book
  • © 1988

Overview

Editors:
  1. Stig Lundqvist

    1. Chalmers University of Technology, Göteborg, Sweden

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  2. Norman H. March

    1. University of Oxford, Oxford, England

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    You can also search for this editor in PubMed   Google Scholar

  3. Mario P. Tosi

    1. International Center for Theoretical Physics, Trieste, Italy

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Part of the book series: Physics of Solids and Liquids (PSLI)

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Table of contents (17 chapters)

  1. Front Matter

    Pages i-xvii
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  2. Chaos, Order, Patterns, Fractals—An Overview

    • S. Lundqvist
    Pages 1-37

  3. An Introduction to the Properties of One-Dimensional Difference Equations

    • G. Rowlands
    Pages 39-62

  4. Spectral Transform and Solitons: How to Solve and Investigate Nonlinear Evolution Equations

    • F. Calogero, A. Degasperis
    Pages 63-137

  5. Homogeneous Isothermal Oscillations and Spatiotemporal Organization in Chemical Reactions

    • P. De Kepper
    Pages 139-166

  6. Synergetics—From Physics to Biology

    • H. Haken
    Pages 167-192

  7. Instabilities and Chaos in Lasers: Introduction to Hyperchaos

    • F. T. Arecchi
    Pages 193-224

  8. Nonlinear Optics of Bistability and Pulse Propagation

    • R. Loudon
    Pages 225-252

  9. Electron and Phonon Instabilities

    • P. N. Butcher
    Pages 253-275

  10. Fractals in Physics: Introductory Concepts

    • L. Pietronero
    Pages 277-294

  11. Phase Transitions

    • R. B. Stinchcombe
    Pages 295-340

  12. Classical Chaos and Quantum Eigenvalues

    • M. V. Berry
    Pages 341-348

  13. Renormalization Description of Transitions to Chaos

    • P. Cvitanović
    Pages 349-360

  14. Order and Chaos in Hamiltonian Systems

    • I. C. Percival
    Pages 361-386

  15. Elementary Symbolic Dynamics

    • Hao Bai-Lin
    Pages 387-422

  16. Nonlinear Mechanical Properties

    • G. Caglioti, C. E. Bottani
    Pages 423-446

  17. Reconstruction of Piecewise Smooth Surfaces Using Simple Analog and Hybrid Networks

    • J. M. Hutchinson, C. Koch
    Pages 447-455

  18. The Slaving Principle of Synergetics—An Outline

    • H. Haken, A. Wunderlin
    Pages 457-463

  19. Back Matter

    Pages 465-469
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Keywords

About this book

This volume is concerned with the theoretical description of patterns and instabilities and their relevance to physics, chemistry, and biology. More specifically, the theme of the work is the theory of nonlinear physical systems with emphasis on the mechanisms leading to the appearance of regular patterns of ordered behavior and chaotic patterns of stochastic behavior. The aim is to present basic concepts and current problems from a variety of points of view. In spite of the emphasis on concepts, some effort has been made to bring together experimental observations and theoretical mechanisms to provide a basic understanding of the aspects of the behavior of nonlinear systems which have a measure of generality. Chaos theory has become a real challenge to physicists with very different interests and also in many other disciplines, of which astronomy, chemistry, medicine, meteorology, economics, and social theory are already embraced at the time of writing. The study of chaos-related phenomena has a truly interdisciplinary charac­ ter and makes use of important concepts and methods from other disciplines. As one important example, for the description of chaotic structures the branch of mathematics called fractal geometry (associated particularly with the name of Mandelbrot) has proved invaluable. For the discussion of the richness of ordered structures which appear, one relies on the theory of pattern recognition. It is relevant to mention that, to date, computer studies have greatly aided the analysis of theoretical models describing chaos.

Editors and Affiliations

  • Chalmers University of Technology, Göteborg, Sweden

    Stig Lundqvist

  • University of Oxford, Oxford, England

    Norman H. March

  • International Center for Theoretical Physics, Trieste, Italy

    Mario P. Tosi

Bibliographic Information

  • Book Title: Order and Chaos in Nonlinear Physical Systems

  • Editors: Stig Lundqvist, Norman H. March, Mario P. Tosi

  • Series Title: Physics of Solids and Liquids

  • DOI: https://doi.org/10.1007/978-1-4899-2058-4

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1988

  • Hardcover ISBN: 978-0-306-42847-0Published: 31 July 1988

  • Softcover ISBN: 978-1-4899-2060-7Published: 17 June 2013

  • eBook ISBN: 978-1-4899-2058-4Published: 11 November 2013

  • Edition Number: 1

  • Number of Pages: XVII, 469

  • Topics: Theoretical, Mathematical and Computational Physics

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