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This textbook gives a contemporary account of singularity theory and its principal application, bifurcation theory.
List 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.
About the author
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).
