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"Suitable for advanced undergraduates, postgraduates and researchers, this self-contained textbook provides an introduction to the mathematics lying at the foundations of bifurcation theory. The theory is built up gradually, beginning with the well-developed approach to singularity theory through right-equivalence. The text proceeds with contact equivalence of map-germs and finally presents the path formulation of bifurcation theory. This formulation, developed partly by the author, is more general and more flexible than the original one dating from the 1980s. A series of appendices discuss standard background material, such as calculus of several variables, existence and uniqueness theorems for ODEs, and some basic material on rings and modules. Based on the author's own teaching experience, the book contains numerous examples and illustrations. The wealth of end-of-chapter problems develop and reinforce understanding of the key ideas and techniques: solutions to a selection are provided"--

Bifurcation theory --- Catastrophes (Mathematics)

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Nonlinear science has a very broad scope and the aim of this volume of lectures is to introduce different aspects of this vast domain to research students whose studies are necessarily concentrated on only one. The lectures given at summer schools in France between 1997 and 1999, describe analytical, geometrical and experimental approaches to subjects as diverse as turbulence, elasticity, physiology, classical mechanics, quantum chaos, water waves and the laser cooling of atoms.

Nonlinear theories. --- Mathematical physics. --- Physical mathematics --- Physics --- Nonlinear problems --- Nonlinearity (Mathematics) --- Calculus --- Mathematical analysis --- Mathematical physics --- Mathematics

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Geometry, Differential. --- Differentiable dynamical systems. --- Mechanics, Analytic. --- Géométrie différentielle --- Dynamique différentiable --- Mécanique analytique --- Géométrie différentielle --- Dynamique différentiable --- Mécanique analytique