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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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The lectures in this 2005 book are intended to bring young researchers to the current frontier of knowledge in geometrical mechanics and dynamical systems. They succinctly cover an unparalleled range of topics from the basic concepts of symplectic and Poisson geometry, through integrable systems, KAM theory, fluid dynamics, and symmetric bifurcation theory. The lectures are based on summer schools for graduate students and postdocs and provide complementary and contrasting viewpoints of key topics: the authors cut through an overwhelming amount of literature to show young mathematicians how to get to the core of the various subjects and thereby enable them to embark on research careers.

Mechanics, Analytic. --- Geometry, Differential. --- Differentiable dynamical systems. --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics --- Differential geometry --- Analytical mechanics --- Kinetics