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Singularity theory and an introduction to catastrophe theory

Author: Yung-Chen Lu
Publisher: New York : Springer-Verlag, ©1976.
Series: Universitext.
Edition/Format:   Print book : English : 2d corr. printView all editions and formats
Summary:

In April, 1975, I organised a conference at the Battelle Research Center, Seattle, Washington on the theme "Structural stability, catastrophe theory and their applications in the sciences".

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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Yung-Chen Lu
ISBN: 038790221X 9780387902210 354090221X 9783540902218
OCLC Number: 422091055
Description: xii, 199 p. : ill. ; 24 cm.
Contents: 1 Introduction to Singularity Theory with Historical Remarks.- 1. Introduction with naive discussion.- 2. Elementary definitions.- 3. Genericity.- 4. Stability.- 5. Singularities.- 2 On Singularities of Mappings from the Plane into the Plane.- 1. Introduction.- 2. Jet spaces.- 3. Transversality.- 4. Morse Lemma - the genericity aspect.- 5. Characterization of folds and cusps.- 6. Whitney's Theorem.- 7. The proof of Theorem 6.1.- 8. The proof of Theorem 6.2.- 3 Unfoldings of Mappings.- 1. Introduction.- 2. Germs of mappings.- 3. Finitely determined germs.- 4. Universal unfolding.- 5. Thom's Classification Theorem.- 4 Catastrophe Theory.- 1. Introduction.- 2. Naive discussion with illustrative examples.- 3. The elementary catastrophes.- 4. Types of elementary catastrophes.- 5 Thom-Whitney Stratification Theory.- 1. Introduction.- 2. Examples.- 3. Regularity conditions of H. Whitney.- 4. Fundamental theorems.- 5. Ratio test.- 6 CO-Sufficiency of Jets.- 1. Introduction.- 2. Criterion of CO- and v-sufficiency of jets in Jr(n,l).- 3. Degree of CO-sufficiency.- 4. Sufficiency of jets in Jr(n,p).- Appendix I - Thom's Three Basic Principles.- Appendix II - The Proof of Thom's Classification Theorem.- Further Reading.
Series Title: Universitext.
Responsibility: Yung-chen Lu.

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