Chaotic Motions in Nonlinear Dynamical Systems

  • W. Szemplińska-Stupnicka
  • G. Iooss
  • F. C. Moon

Part of the International Centre for Mechanical Sciences book series (CISM, volume 298)

Table of contents

  1. Front Matter
    Pages i-v
  2. F. Moon
    Pages 1-50
  3. W. Szemplinska-Stupnicka
    Pages 51-136

About this book

Introduction

Discoveries of chaotic, unpredictable behaviour in physical deterministic systems has brought about new analytic and experimental techniques in dynamics. The modern study of the new phenomena requires the analyst to become familiar with experiments (at least with numerical ones), since chaotic solutions cannot be written down, and it requires the experimenter to master the new concepts of the theory of nonlinear dynamical systems. This book is unique in that it presents both viewpoints: the viewpoint of the analyst and of the experimenter. In the first part F. Moon outlines the new experimental techniques which have emerged from the study of chaotic vibrations. These include Poincaré sections, fractial dimensions and Lapunov exponents. In the text by W. Szemplinska-Stupnicka the relation between the new chaotic phenomena and classical perturbation techniques is explored for the first time. In the third part G. Iooss presents methods of analysis for the calculations of bifurcations in nonlinear systems based on modern geometric mathematical concepts.

Keywords

bifurcation dynamical system dynamical systems dynamics nonlinear dynamics nonlinear system solution Vibration

Authors and affiliations

  • W. Szemplińska-Stupnicka
    • 1
  • G. Iooss
    • 2
  • F. C. Moon
    • 3
  1. 1.Polish Academy of SciencesPoland
  2. 2.Université de NiceFrance
  3. 3.Cornell UniversityUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-7091-2596-0
  • Copyright Information CISM Udine 1988
  • Publisher Name Springer, Vienna
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-211-82062-9
  • Online ISBN 978-3-7091-2596-0
  • Series Print ISSN 0254-1971
  • Series Online ISSN 2309-3706
  • About this book
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