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Differentiable Germs and Catastrophes : London Mathematical Society Lecture Note Series - Theodor Brocker

Differentiable Germs and Catastrophes

London Mathematical Society Lecture Note Series

By: Theodor Brocker, L. Lander (Translator)

Paperback Published: 15th September 1975
ISBN: 9780521206815
Number Of Pages: 188

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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.

Foreword
Germs with constant rank
Regular values
Construction of differentiable maps
Germs and jets
The division theorem
The preparation theorem
Symmetric germs
Mappings of the plane into the plane
Boardman-Thom singularities
The quadratic differential
Finitely determined germs
Some elementary algebraic geometry
Tougeron's theory
The universal unfolding of a singularity
The seven elementary catastrophes
Proof of the main theorem on universal unfoldings
Pictures of the seven elementary catastrophes
Further reading
Indices
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780521206815
ISBN-10: 0521206812
Series: London Mathematical Society Lecture Note Series
Audience: Tertiary; University or College
Format: Paperback
Language: English
Number Of Pages: 188
Published: 15th September 1975
Publisher: Cambridge University Press
Country of Publication: GB
Dimensions (cm): 22.9 x 15.2  x 1.1
Weight (kg): 0.28