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Cell-to-Cell Mapping

A Method of Global Analysis for Nonlinear Systems

  • Book
  • © 1987

Overview

Authors:
  1. C. S. Hsu

    1. Department of Mechanical Engineering, University of California, Berkeley, USA

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Part of the book series: Applied Mathematical Sciences (AMS, volume 64)

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Table of contents (14 chapters)

  1. Front Matter

    Pages i-xii
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  2. Introduction and Overview

    • C. S. Hsu
    Pages 1-15

  3. Point Mapping

    • C. S. Hsu
    Pages 16-47

  4. Analysis of Impulsive Parametric Excitation Problems by Point Mapping

    • C. S. Hsu
    Pages 48-84

  5. Cell State Space and Simple Cell Mapping

    • C. S. Hsu
    Pages 85-97

  6. Singularities of Cell Functions

    • C. S. Hsu
    Pages 98-119

  7. A Theory of Index for Cell Functions

    • C. S. Hsu
    Pages 120-126

  8. Characteristics of Singular Entities of Simple Cell Mappings

    • C. S. Hsu
    Pages 127-138

  9. Algorithms for Simple Cell Mappings

    • C. S. Hsu
    Pages 139-152

  10. Examples of Global Analysis by Simple Cell Mapping

    • C. S. Hsu
    Pages 153-207

  11. Theory of Generalized Cell Mapping

    • C. S. Hsu
    Pages 208-243

  12. Algorithms for Analyzing Generalized Cell Mappings

    • C. S. Hsu
    Pages 244-276

  13. An Iterative Method, from Large to Small

    • C. S. Hsu
    Pages 277-305

  14. Study of Strange Attractors by Generalized Cell Mapping

    • C. S. Hsu
    Pages 306-330

  15. Other Topics of Study Using the Cell State Space Concept

    • C. S. Hsu
    Pages 331-334

  16. Back Matter

    Pages 335-353
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Keywords

About this book

For many years, I have been interested in global analysis of nonlinear systems. The original interest stemmed from the study of snap-through stability and jump phenomena in structures. For systems of this kind, where there exist multiple stable equilibrium states or periodic motions, it is important to examine the domains of attraction of these responses in the state space. It was through work in this direction that the cell-to-cell mapping methods were introduced. These methods have received considerable development in the last few years, and have also been applied to some concrete problems. The results look very encouraging and promising. However, up to now, the effort of developing these methods has been by a very small number of people. There was, therefore, a suggestion that the published material, scattered now in various journal articles, could perhaps be pulled together into book form, thus making it more readily available to the general audience in the field of nonlinear oscillations and nonlinear dynamical systems. Conceivably, this might facilitate getting more people interested in working on this topic. On the other hand, there is always a question as to whether a topic (a) holds enough promise for the future, and (b) has gained enough maturity to be put into book form. With regard to (a), only the future will tell. With regard to (b), I believe that, from the point of view of both foundation and methodology, the methods are far from mature.

Authors and Affiliations

  • Department of Mechanical Engineering, University of California, Berkeley, USA

    C. S. Hsu

Bibliographic Information

  • Book Title: Cell-to-Cell Mapping

  • Book Subtitle: A Method of Global Analysis for Nonlinear Systems

  • Authors: C. S. Hsu

  • Series Title: Applied Mathematical Sciences

  • DOI: https://doi.org/10.1007/978-1-4757-3892-6

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1987

  • Hardcover ISBN: 978-0-387-96520-8Published: 13 August 1987

  • Softcover ISBN: 978-1-4419-3083-5Published: 01 December 2010

  • eBook ISBN: 978-1-4757-3892-6Published: 09 March 2013

  • Series ISSN: 0066-5452

  • Series E-ISSN: 2196-968X

  • Edition Number: 1

  • Number of Pages: XII, 354

  • Topics: Analysis, Theoretical, Mathematical and Computational Physics

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