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 phemena requires the analyst to become familiar with experiments (at least with numerical ones), since chaotic solutions cant be written down, and it requires the experimenter to master the new concepts of the theory of nlinear 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 Poincare sections, fractial dimensions and Lapuv exponents. In the text by W. Szemplinska-Stupnicka the relation between the new chaotic phemena 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 nlinear systems based on modern geometric mathematical concepts.
Francis C. Moon, Gerard Iooss, Wanda Szemplinska-Stupnicka