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Differentiable Germs and Catastrophes Theodor Broecker

Differentiable Germs and Catastrophes par Theodor Broecker

Differentiable Germs and Catastrophes Theodor Broecker


Résumé

This book gives a fairly elementary introduction to the local theory of differentiable mappings and is suitable as a text for courses to graduates and advanced undergraduates.

Differentiable Germs and Catastrophes Résumé

Differentiable Germs and Catastrophes Theodor Broecker

These notes give a fairly elementary introduction to the local theory of differentiable mappings. Sard's Theorem and the Preparation Theorem of Malgrange and Mather are the basic tools and these are proved first. There follows a number of illustrations including: the local part of Whitney's Theorem on mappings of the plane into the plane, quadratic differentials, the Instability Theorem of Thom, one of Mather's theorems on finite determinacy and a glimpse of the theory of Toujeron. The later part of the book develops Mather's theory of unfoldings of singularities. Its application to Catastrophe theory is explained and the Elementary Catastrophes are illustrated by many pictures. The book is suitable as a text for courses to graduates and advanced undergraduates but may also be of interest to mathematical biologists and economists.

Sommaire

1. Foreword; 1. Germs with constant rank; 2. Regular values; 3. Construction of differentiable maps; 4. Germs and jets; 5. The division theorem; 6. The preparation theorem; 7. Symmetric germs; 8. Mappings of the plane into the plane; 9. Boardman-Thom singularities; 10. The quadratic differential; 11. Finitely determined germs; 12. Some elementary algebraic geometry; 13. Tougeron's theory; 14. The universal unfolding of a singularity; 15. The seven elementary catastrophes; 16. Proof of the main theorem on universal unfoldings; 17. Pictures of the seven elementary catastrophes; Further reading; Indices.

Informations supplémentaires

CIN0521206812G
9780521206815
0521206812
Differentiable Germs and Catastrophes Theodor Broecker
Occasion - Bon état
Broché
Cambridge University Press
19750717
188
N/A
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