
- English
- PDF
- Available on iOS & Android
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.
Frequently asked questions
- Essential is ideal for learners and professionals who enjoy exploring a wide range of subjects. Access the Essential Library with 800,000+ trusted titles and best-sellers across business, personal growth, and the humanities. Includes unlimited reading time and Standard Read Aloud voice.
- Complete: Perfect for advanced learners and researchers needing full, unrestricted access. Unlock 1.4M+ books across hundreds of subjects, including academic and specialized titles. The Complete Plan also includes advanced features like Premium Read Aloud and Research Assistant.
Please note we cannot support devices running on iOS 13 and Android 7 or earlier. Learn more about using the app.
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