- 190 pages
- English
- PDF
- Available on iOS & Android
eBook - PDF
Differentiable Germs and Catastrophes
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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Information
Table of contents
- Cover
- Series Page
- Title
- Copyright
- Contents
- Dedication
- 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-Thorn 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
- List of symbols
- Index
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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 Mathematics & Topology. We have over one million books available in our catalogue for you to explore.