James Montaldi (University of Manchester)

Singularities, Bifurcations and Catastrophes

• Broschiertes Buch

Produktbeschreibung

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.

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Produktdetails

• Verlag: Cambridge University Press
• Seitenzahl: 448
• Erscheinungstermin: 15. Juli 2021
• Englisch
• Abmessung: 239mm x 167mm x 25mm
• Gewicht: 860g
• ISBN-13: 9781316606216
• ISBN-10: 131660621X
• Artikelnr.: 61316185

Autorenporträt

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).

Inhaltsangabe

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.