Skip to main content
SpringerLink
Log in
Book cover

Dimensions and Entropies in Chaotic Systems

Quantification of Complex Behavior Proceeding of an International Workshop at the Pecos River Ranch, New Mexico, September 11–16, 1985

  • Conference proceedings
  • © 1986

Overview

Editors:
  1. Gottfried Mayer-Kress

    1. Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, USA

    View editor publications

    You can also search for this editor in PubMed   Google Scholar

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

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (29 papers)

  1. Front Matter

    Pages II-IX
    Download chapter PDF

  2. Introduction

    1. Front Matter

      Pages 1-1
      Download chapter PDF

    2. Introductory Remarks

      • G. Mayer-Kress
      Pages 2-5

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

    1. Front Matter

      Pages 61-61
      Download chapter PDF

    2. Lorenz Cross-Sections and Dimension of the Double Rotor Attractor

      • E. J. Kostelich, J. A. Yorke
      Pages 62-66

    3. On the Fractal Dimension of Filtered Chaotic Signals

      • R. Badii, A. Politi
      Pages 67-73

    4. Efficient Algorithms for Computing Fractal Dimensions

      • F. Hunt, F. Sullivan
      Pages 74-81

    5. Using Mutual Information to Estimate Metric Entropy

      • A. M. Fraser
      Pages 82-91

  5. Computation of Lyapunov Exponents

    1. Front Matter

      Pages 93-93
      Download chapter PDF

    2. Intermediate Length Scale Effects in Lyapunov Exponent Estimation

      • A. Wolf, J. A. Vastano
      Pages 94-99

    3. Comparison of Algorithms for Determining Lyapunov Exponents from Experimental Data

      • J. A. Vastano, E. J. Kostelich
      Pages 100-107

    4. A Measure of Chaos for Open Flows

      • R. J. Deissler, K. Kaneko
      Pages 108-111

  6. Reliability, Accuracy and Date-Requirements of Different Algorithms

    1. Front Matter

      Pages 113-113
      Download chapter PDF
Back to top

Keywords

About this book

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.

Editors and Affiliations

  • Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, USA

    Gottfried Mayer-Kress

Bibliographic Information

Publish with us

Policies and ethics

Back to top

Search

Navigation