Singularity Theory and an Introduction to Catastrophe Theory
Springer-Verlag New York Inc.
978-0-387-90221-0 (ISBN)
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.
Reihe/Serie | Universitext |
---|---|
Zusatzinfo | XII, 200 p. |
Verlagsort | New York, NY |
Sprache | englisch |
Maße | 170 x 244 mm |
Themenwelt | Mathematik / Informatik ► Mathematik |
Naturwissenschaften ► Physik / Astronomie ► Allgemeines / Lexika | |
ISBN-10 | 0-387-90221-X / 038790221X |
ISBN-13 | 978-0-387-90221-0 / 9780387902210 |
Zustand | Neuware |
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