Chapter 6. Strange Attractors in Dissipative Dynamical Systems

  1. Prof. Dr. H. G. Schuster1 and
  2. Lecturer Wolfram Just2

Published Online: 23 AUG 2005

DOI: 10.1002/3527604804.ch6

Deterministic Chaos: An Introduction, Fourth Edition

Deterministic Chaos: An Introduction, Fourth Edition

How to Cite

Schuster, H. G. and Just, W. (2005) Strange Attractors in Dissipative Dynamical Systems, in Deterministic Chaos: An Introduction, Fourth Edition, Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim, FRG. doi: 10.1002/3527604804.ch6

Author Information

  1. 1

    Christian Albrecht University Kiel, Department of Theoretical Physics, Germany

  2. 2

    Queen Mary/University of London, School of Mathematical Sciences, United Kingdom

Publication History

  1. Published Online: 23 AUG 2005
  2. Published Print: 26 JAN 2005

ISBN Information

Print ISBN: 9783527404155

Online ISBN: 9783527604807

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Keywords:

  • chaos;
  • deterministic chaos;
  • strange attractors;
  • dissipative dynamical systems;
  • attractors;
  • Baker's transformation;
  • Hénon map;
  • Kolmogorov entropy;
  • Liapunov exponents;
  • chaotic system;
  • singularities in the invariant density;
  • generalized entropies;
  • entropy;
  • Kaplan–Yorke conjecture;
  • fractal boundaries

Summary

This chapter contains sections titled:

  • Introduction and Definition of Strange Attractors

    • Baker's Transformation

    • Dissipative Hénon Map

  • The Kolmogorov Entropy

    • Definition of K

    • Connection of K to the Liapunov Exponents

    • Average Time over which the State of a Chaotic System can be Predicted

  • Characterization of the Attractor by a Measured Signal

    • Reconstruction of the Attractor from a Time Series

    • Generalized Dimensions and Distribution of Singularities in the Invariant Density

    • Generalized Entropies and Fluctuations around the K-Entropy

    • Kaplan–Yorke Conjecture

  • Pictures of Strange Attractors and Fractal Boundaries