Differentiable germs and catastrophes

書誌事項

Differentiable germs and catastrophes

Th. Bröcker & L. Lander ; [translated by L. Lander]

(London Mathematical Society lecture note series, 17)

Cambridge University Press, c1975

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注記

"A small number of copies of the German text were printed ... under the title: Der Regensburger Trichter, Band 3, Differenzierbare Abbildungen."

Bibliography: p. 172-175

Includes index

内容説明・目次

内容説明

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.

目次

  • 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.

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