Singularities, Bifurcations and Catastrophes
“Singularities, Bifurcations and Catastrophes” by James Montaldi is a comprehensive textbook published by Cambridge University Press on June 24, 2021. This 448-page edition is written in English and is designed for advanced undergraduates, postgraduates, and researchers interested in the mathematical foundations of bifurcation theory. The book introduces singularity theory through right-equivalence and progresses to contact equivalence of map-germs, culminating in a more general and flexible path formulation of bifurcation theory.
Readers will find a self-contained exploration of key mathematical concepts, supported by numerous examples and illustrations that enhance understanding. The text includes a series of appendices covering essential background material, such as calculus of several variables and existence and uniqueness theorems for ordinary differential equations. Additionally, the book features a wealth of end-of-chapter problems to reinforce the key ideas and techniques discussed, with solutions provided for a selection of these problems. This resource serves as a valuable tool for those delving into mathematics, topology, geometry, and algebraic topics.
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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.
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