Singularities, Bifurcations and Catastrophes

This textbook gives a contemporary account of singularity theory and its principal application, bifurcation theory.

Suitable for advanced undergraduates, postgraduates and researchers, this text introduces the key ideas of modern singularity theory and develops an approach to the foundations of bifurcation theory, which is more flexible than the standard one. It contains numerous examples and problems, with solutions to a selection of them.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.