Order and Chaos in Nonlinear Physical Systems

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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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.

• Soliton
• chaos
• chaos theory
• dynamics
• fractal
• geometry
• mathematics

• 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

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