Author | Lu, Yung-Chen. author |
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Title | Singularity Theory and an Introduction to Catastrophe Theory [electronic resource] / by Yung-Chen Lu |
Imprint | New York, NY : Springer New York, 1976 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-9909-7 |
Descript | XII, 200 p. online resource |
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 โ the genericity aspect -- 5. Characterization of folds and cusps -- 6. Whitneyโs 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. Thomโs 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 โ Thomโs Three Basic Principles -- Appendix II โ The Proof of Thomโs Classification Theorem -- Further Reading