Singularities, Bifurcations and Catastrophes

ISBN-13: 9781316606216 / Angielski / Miękka / 2021 / 448 str.

James Montaldi

Opis

This textbook gives a contemporary account of singularity theory and its principal application, bifurcation theory.

Recenzje

'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

Spis treści

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.