Chaotic Motions in Nonlinear Dynamical Systems

✍ Scribed by W. Szemplińska-Stupnicka, G. Iooss, F. C. Moon (auth.)

• Publisher: Springer-Verlag Wien
• Year: 1988
• Tongue: English
• Leaves: 198
• Series: International Centre for Mechanical Sciences 298
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages i-v
Experiments in Chaotic Dynamics....Pages 1-50
Chaotic and Regular Motion in Nonlinear Vibrating Systems....Pages 51-136
Local Techniques in Bifurcation Theory and Nonlinear Dynamics....Pages 137-193

✦ Subjects

Appl.Mathematics/Computational Methods of Engineering; Mechanics; Mathematical Methods in Physics; Numerical and Computational Physics; Acoustics; Manifolds and Cell Complexes (incl. Diff.Topology)