Singularities, Bifurcations and Catastrophes
Singularities, Bifurcations and Catastrophes
Experience the eBook and the associated online resources on our new Higher Education website.
Go to site
For other formats please stay on this page.
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.
- Builds up the mathematical background for a new approach to the foundations of bifurcation theory
- The first two parts are of independent interest and can be the basis for an advanced undergraduate or graduate course
- Contains many colour figures and exercises, with some solutions included and a manual for selected others available for teachers
Reviews & endorsements
'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
'This mostly self-contained and user-friendly textbook, aimed at advanced undergraduate level and above, provides a careful and accessible introduction to methods of singularity theory that underlie much of local bifurcation theory.' D. R. J. Chillingworth, MathSciNet
Product details
June 2021Hardback
9781107151642
446 pages
251 × 177 × 25 mm
0.95kg
Available
Table of Contents
- Preface
- 1. What's It All About?
- Part I. Catastrophe Theory
- 2. Families of Functions
- 3. The Ring of Germs of Smooth Functions
- 4. Right Equivalence
- 5. Finite Determinacy
- 6. Classification of the Elementary Catastrophes
- 7. Unfoldings and Catastrophes
- 8. Singularities of Plane Curves
- 9. Even Functions
- Part II. Singularity Theory
- 10. Families of Maps and Bifurcations
- 11. Contact Equivalence
- 12. Tangent Spaces
- 13. Classification for Contact Equivalence
- 14. Contact Equivalence and Unfoldings
- 15. Geometric Applications
- 16. Preparation Theorem
- 17. Left-Right Equivalence
- Part III. Bifurcation Theory
- 18. Bifurcation Problems and Paths
- 19. Vector Fields Tangent to a Variety
- 20. Kv-equivalence
- 21. Classification of Paths
- 22. Loose Ends
- 23. Constrained Bifurcation Problems
- Part IV. Appendices
- A. Calculus of Several Variables
- B. Local Geometry of Regular Maps
- C. Differential Equations and Flows
- D. Rings, Ideals and Modules
- E. Solutions to Selected Problems.
