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Dimensions and Entropies in Chaotic Systems

Quantification of Complex Behavior

  • Gottfried Mayer-Kress

Part of the Springer Series in Synergetics book series (SSSYN, volume 32)

Table of contents

  1. Front Matter
    Pages II-IX
  2. Introduction

    1. Front Matter
      Pages 1-1
    2. G. Mayer-Kress
      Pages 2-5
  3. General Theory, Mathematical Aspects of Dimensions, Basic Problems

  4. Numerical and Experimental Problems in the Calculation of Dimensions and Entropies

    1. Front Matter
      Pages 61-61
  5. Computation of Lyapunov Exponents

    1. Front Matter
      Pages 93-93
    2. R. J. Deissler, K. Kaneko
      Pages 108-111
  6. Reliability, Accuracy and Date-Requirements of Different Algorithms

  7. Analysing Spatio Temporal Chaos

    1. Front Matter
      Pages 149-149
    2. A. Brandstater, H. L. Swinney, G. T. Chapman
      Pages 150-157
  8. Experimental Results and Applications

    1. Front Matter
      Pages 179-179
    2. H. Haucke, R. E. Ecke, J. C. Wheatley
      Pages 198-206
    3. J. Stavans, S. Thomae, A. Libchaber
      Pages 207-214
    4. P. H. Carter, R. Cawley, A. L. Licht, J. A. Yorke, M. S. Melnik
      Pages 215-221
    5. K. R. Sreenivasan
      Pages 222-230
    6. A. M. Albano, N. B. Abraham, G. C. de Guzman, M. F. H. Tarroja, D. K. Bandy, R. S. Gioggia et al.
      Pages 231-240
    7. S. P. Layne, G. Mayer-Kress, J. Holzfuss
      Pages 246-256
  9. Back Matter
    Pages 257-257

About these proceedings

Introduction

These proceedings contain the papers contributed to the International Work­ shop on "Dimensions and Entropies in Chaotic Systems" at the Pecos River Conference Center on the Pecos River Ranch in Spetember 1985. The work­ shop was held by the Center for Nonlinear Studies of the Los Alamos National Laboratory. At the Center for Nonlinear Studies the investigation of chaotic dynamics and especially the quantification of complex behavior has a long tradition. In spite of some remarkable successes, there are fundamental, as well as nu­ merical, problems involved in the practical realization of these algorithms. This has led to a series of publications in which modifications and improve­ ments of the original methods have been proposed. At present there exists a growing number of competing dimension algorithms but no comprehensive review explaining how they are related. Further, in actual experimental ap­ plications, rather than a precise algorithm, one finds frequent use of "rules of thumb" together with error estimates which, in many cases, appear to be far too optimistic. Also it seems that questions like "What is the maximal dimension of an attractor that one can measure with a given number of data points and a given experimental resolution?" have still not been answered in a satisfactory manner for general cases.

Keywords

algorithms chaos complex system complex systems dynamical systems entropy system turbulence

Editors and affiliations

  • Gottfried Mayer-Kress
    • 1
  1. 1.Center for Nonlinear StudiesLos Alamos National LaboratoryLos AlamosUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-71001-8
  • Copyright Information Springer-Verlag Berlin Heidelberg 1986
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-71003-2
  • Online ISBN 978-3-642-71001-8
  • Series Print ISSN 0172-7389
  • Buy this book on publisher's site
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