Singularities, Bifurcations and Catastrophes

James Montaldi (University of Manchester)

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English

Cambridge University Press
24 June 2021

Algebraic geometry; Topology

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.

By: James Montaldi (University of Manchester)
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Dimensions: Height: 251mm, Width: 177mm, Spine: 25mm
Weight: 950g
ISBN: 9781107151642
ISBN 10: 1107151643
Pages: 446
Publication Date: 24 June 2021
Audience: Professional and scholarly , Undergraduate
Format: Hardback
Publisher's Status: Active

James Montaldi is Reader in Mathematics at University of Manchester. He has worked both in theoretical aspects of singularity theory as well as applications to dynamical systems, and co-edited the books: Geometric Mechanics and Symmetry: The Peyresq Lectures (Cambridge, 2005), Peyresq Lectures in Nonlinear Systems (2000), and Singularity Theory and its Applications Part 1 (1991).

Reviews for Singularities, Bifurcations and Catastrophes

'This beautiful book is in fact a course which can be viewed as addressed to undergraduate and graduate students, to junior and senior researchers, to the teaching staff (faculty), and to other people interested in the ﬁeld.' Vladimir Răsvan, European Mathematical Society