Experiments in Chaotic Dynamics
The discovery of deterministic chaotic vibrations in nonlinear dynamical systems has led to new mathematical ideas and analytical techniques in nonlinear dynamics. Along with these new ideas has come a host of new experimental tools to analyze vibrations
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CHAOTIC MOTIONS IN NONLINEAR DYNAMICAL SYSTEMS
W. SZEMPLINSKA-STUPNICKA POLISH ACADEMY OF SCIENCES
G. IOOSS UNIVERSITE DE NICE
F.C. MOON CORNELL UNIVERSITY
SPRINGER-VERLAG WIEN GMBH
SCIENCES
I.e spese di stampa di questo volume sono in parte coperte da contributi del Consiglio Nazionale delle Ricerche.
Tirls volume contains 88 illustrations.
Tirls work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks.
© 1988 by Springer-Verlag Wien Originally published by Springer Verlag Wien-New York in 1988
ISBN 978-3-211-82062-9 DOI 10.1007/978-3-7091-2596-0
ISBN 978-3-7091-2596-0 (eBook)
PREFACE
The discovery of new types of dynamic behavior in physical systems in the last decade has brought about new analytic and experimental techniques in dynamics. Principal amongst these new discoveries is the existence of chaotic, unpredictable behavior in many nonlinear deterministic systems. Observations of chaotic and prechaotic behavior have been observed in all areas of classical physics including solid and fluid mechanics, thermo-fluid phenomena, electromagnetic systems and in the area of acoustics. The lectures presented in this book, look at the field ofchaotic and nonlinear dynamics from three different points of view. In the first set of lectures F. Moon outlines many of the new experimental techniques which have emerged from the study of chaotic vibrations. These include Poincare sections, fractal dimensions and Lyaponov exponents. In the text by W. Szemplinska-Stupnicka, the relation between the new chaotic phenomena and classical perturbation techniques of nonlinear vibration is explored for the first time. Chaotic phenomena is often preceded by a series of bifurcations including sub harmonic and limit cycle or Hopf bifurcations. Finally, in the third set of lecture notes G. Iooss presents methods of analysis for the calculation of bifurcation in nonlinear systems based on molecular geometric mathematical concepts. The modern study ofnonlinear dynamics is unique in the field ofapplied mathematics since it
requires the analyst to become familiar with experiments (at least numerical ones) since chaotic solutions cannot be written down, and it requires the experimentalist to master the next concepts in the theory of nonlinear dynamical systems. This book is unique in that it presents both the viewpoint of the analyst and the experimenter in nonlinear and chaotic dynamics. It should be of interest to engineers, physicists and applied mathematicians interested in chaotic and stochastic phenomena. It is indeed fitting that these lectures were given in Udine, Italy near where Galileo made his earlier discoveries in dynamics. It is exciting to observe that often many centuries ago new studies in dynamics were being made that will have an important impact in both classical physics and applied science.
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