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Chaotic Dynamics

Theory and Practice

  • Book
  • © 1992

Overview

Editors:
  1. T. Bountis

    1. University of Patras, Patras, Greece

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Part of the book series: NATO Science Series B: (NSSB, volume 298)

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Table of contents (37 chapters)

  1. Front Matter

    Pages i-xii
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  2. Chaotic Dynamics: Theory

    1. Complexity, Control and Data Representaion

      1. Complexity and Unpredictable Scaling of Hierarchical Structures
        • R. Badii
        Pages 1-19
      2. Asymptotic State Estimation Using Observers in Dynamical and Control Systems
        • I. Kupka
        Pages 21-31
      3. Learning Optimal Representations
        • Joseph L. Breeden, Norman H. Packard
        Pages 33-41

    2. Fractals, Multifractals and Analyticity of Normal Forms

      1. Multifractal Coding Measures in Dynamics
        • Giorgio Mantica
        Pages 43-47
      2. Determination of Fractal Dimensions and Generalized Entropies for Strange Attractors
        • Ágnes Fülöp
        Pages 49-52
      3. On the Quaternionic Julia Sets
        • Peter Petek
        Pages 53-58
      4. Perturbation Theory and Analyticity of Normalizing Transformations for Area Preserving Maps
        • Armando Bazzani, Giorgio Turchetti
        Pages 59-70

    3. Integrability, Painleve Property and Singularity Analysis

      1. Note on a Complex Eckhaus Equation
        • Michael F. Jørgensen, Peter L. Christiansen, Silvana de Lillo, Leonor Cruzeiro-Hansson
        Pages 71-73
      2. Integrability of Discrete-Time Systems
        • B. Grammaticos, G. Karra, V. Papageorgiou, A. Ramani
        Pages 75-90
      3. From Weak to Full Painlevé Property via time Singularities Transformations
        • Alain Goriely
        Pages 91-99
      4. The Role of Negative Resonances in the Painlevé Test
        • Allan Fordy, Andrew Pickering
        Pages 101-114
      5. On the Convergence of Series Solutions of Nonintegrable Systems with Algebraic Singularities
        • L. B. Drossos, T. C. Bountis
        Pages 115-128

    4. Statistical Physics, Celestial Mechanics and Cosmology

      1. Phase Transitions within the Fully Developed Chaotic Regime
        • R. Kluiving, H. W. Capel, R. A. Pasmanter
        Pages 129-138
      2. From Dynamical Systems to Local Diffusion Processes
        • Armando Bazzani, Stefano Siboni, Giorgio Turchetti, Sandro Vaienti
        Pages 139-144
      3. Nonintegrability, Separatrices Crossing and Homoclinic Orbits in the Problem of Rotational Motion of a Satellite
        • Andrzej J. Maciejewski, Krzysztof Goździewski
        Pages 145-159
      4. Relativistic Chaos in Robertson-Walker Cosmologies: The Topological Structure of Space-Time and the Microscopic Dynamics
        • Roman Tomaschitz
        Pages 161-175

  3. Chaotic Dynamics: Practice

    1. Controlling Dynamical Systems

      1. Feedback Control of Chaotic Systems
        • Filipe J. Romeiras, Celso Grebogi, Edward Ott, W. P. Dayawansa
        Pages 177-193
      2. The Structure of Basin Boundaries in a Simple Adaptive Control System
        • C. E. Frouzakis, R. A. Adomaitis, I. G. Kevrekidis, M. P. Golden, B. E. Ydstie
        Pages 195-210
      3. A Method For Adaptive Control and Learning in Chaotic Systems
        • Dimitris Vassiliadis
        Pages 211-219
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Keywords

About this book

Many conferences, meetings, workshops, summer schools and symposia on nonlinear dynamical systems are being organized these days, dealing with a great variety of topics and themes -classical and quantum, theoretical and experimental. Some focus on integrability, or discuss the mathematical foundations of chaos. Others explore the beauty of fractals, or examine endless possibilities of applications to problems of physics, chemistry, biology and other sciences. A new scientific discipline has thus emerged, with its own distinct philosophical viewpoint and an impressive arsenal of new methods and techniques, which may be called Chaotic Dynamics. Perhaps its most outstanding achievement so far has been to shed new light on many long­ standing issues involving complicated, irregular or "chaotic" nonlinear phenomena. The concepts of randomness, complexity and unpredictability have been critically re-examined and the fundamental importance of scaling, self-similarity and sensitive dependence on parameters and initial conditions has been firmly established. In this NATO ASI, held at the seaside Greek city of Patras, between July 11- 20, 1991, a serious effort was made to bring together scientists representing many of the different aspects of Chaotic Dynamics. Our main aim was to review recent advances, evaluate the current state of the art and identify some of the more promising directions for research in Chaotic Dynamics.

Editors and Affiliations

  • University of Patras, Patras, Greece

    T. Bountis

Bibliographic Information

  • Book Title: Chaotic Dynamics

  • Book Subtitle: Theory and Practice

  • Editors: T. Bountis

  • Series Title: NATO Science Series B:

  • DOI: https://doi.org/10.1007/978-1-4615-3464-8

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1992

  • Hardcover ISBN: 978-0-306-44247-6Published: 30 November 1992

  • Softcover ISBN: 978-1-4613-6534-1Published: 09 November 2012

  • eBook ISBN: 978-1-4615-3464-8Published: 06 December 2012

  • Series ISSN: 0258-1221

  • Edition Number: 1

  • Number of Pages: XII, 418

  • Topics: Electrical Engineering, Theoretical, Mathematical and Computational Physics

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