Differentiable Germs and Catastrophes
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Differentiable Germs and Catastrophes

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  3. Available on iOS & Android
eBook - PDF

Differentiable Germs and Catastrophes

Book details
Table of contents
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About This Book

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.

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Yes, you can access Differentiable Germs and Catastrophes by Theodor Bröcker, L. Lander in PDF and/or ePUB format, as well as other popular books in Matemáticas & Topología. We have over one million books available in our catalogue for you to explore.

Information

Year
1975
ISBN
9781107107472

Table of contents

  1. Cover
  2. Series Page
  3. Title
  4. Copyright
  5. Contents
  6. Dedication
  7. Foreword
  8. 1· Germs with constant rank
  9. 2· Regular values
  10. 3· Construction of differentiable maps
  11. 4· Germs and jets
  12. 5· The division theorem
  13. 6· The preparation theorem
  14. 7· Symmetric germs
  15. 8· Mappings of the plane into the plane
  16. 9· Boardman-Thorn singularities
  17. 10· The quadratic differential
  18. 11· Finitely determined germs
  19. 12· Some elementary algebraic geometry
  20. 13· Tougeron's theory
  21. 14· The universal unfolding of a singularity
  22. 15· The seven elementary catastrophes
  23. 16· Proof of the main theorem on universal unfoldings
  24. 17· Pictures of the seven elementary catastrophes
  25. Further Reading
  26. List of symbols
  27. Index