Singularities, Bifurcations and Catastrophes

This textbook provides an introduction to the mathematics underlying bifurcation theory,beginning with singularity theory and progressing to contact equivalence and the path formulation. It includes numerous examples and end-of-chapter problems to reinforce understanding.

Format: Hardback
Length: 446 pages
Publication date: 24 June 2021
Publisher: Cambridge University Press

This comprehensive textbook serves as an introduction to the mathematics underlying bifurcation theory, catering to advanced undergraduates, postgraduates, and researchers. It is designed to be self-contained, providing a gradual buildup of the theory. The text begins with a well-developed approach to singularity theory, followed by contact equivalence of map germs. Finally, the path formulation of bifurcation theory is presented, which is more general and flexible than its predecessor from the 1980s.

A series of appendices delve into standard background material, including calculus of several variables, existence and uniqueness theorems for ODEs, and basic concepts of rings and modules. The book is enriched with numerous examples and illustrations, drawn from the author's extensive teaching experience. Additionally, a wealth of end-of-chapter problems are provided, fostering a deeper understanding of the key ideas and techniques. Solutions to a selection of these problems are also offered, aiding in the consolidation of the material learned.

This textbook is an invaluable resource for those seeking to delve into the foundations of bifurcation theory and its applications in various fields of mathematics. Its comprehensive coverage, clear explanations, and abundant exercises make it suitable for both self-study and classroom instruction.

Weight: 964g
Dimension: 177 x 251 x 27 (mm)
ISBN-13: 9781107151642