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.
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.
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.
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.
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