Singularity theory and an introduction to catastrophe theory:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York, NY [u.a.]
Springer
c 1976
|
| Ausgabe: | 2. corr. print. |
| Schriftenreihe: | Universitext
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | 199 S. Ill. |
| ISBN: | 038790221X 354090221X |
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Datensatz im Suchindex
| _version_ | 1804135864087871488 |
|---|---|
| adam_text | CONTENTS
Introduction ix
Acknowledgement xii
Chapter 1 Introduction to Singularity Theory with Historical Remarks ... 1
1. Introduction with naive discussion 1
2. Elementary definitions 3
3. Genericity 12
k. Stability 14
5. Singularities 20
Chapter 2 On Singularities of Mappings from the Plane into the Plane ... 24
1. Introduction 24
2. Jet spaces 25
3. Transversality 26
It . Morse Lemma the genericity aspect 31
5. Characterization of folds and cusps 33
6. Whitney s Theorem 43
7. The proof of Theorem 6.1 44
8. The proof of Theorem 6.2 48
Chapter 3 Unfoldings of Mappings 52
1. Introduction 52
2. Germs of mappings 55
3. Finitely determined germs 60
1+. Universal unfolding 66
5. Thorn s Classification Theorem 85
Chapter k Catastrophe Theory 95
1. Introduction 95
2. Naive discussion with illustrative examples 96
3. The elementary catastrophes 100
k. Types of elementary catastrophes 10U
Chapter 5 Thorn Whitney Stratification Theory 120
1. Introduction 120
2. Examples 122
3. Regularity conditions of H. Whitney 124
k. Fundamental theorems 132
5. Ratio test 138
viii
CONTENTS
Chapter 6 C Sufficiency of Jets 142
1. Introduction 142
2. Criterion of C° and v sufficiency of jets in Jr(n,l) 147
3. Degree of C° sufficiency 155
k . Sufficiency of jets in Jr(n,p) 161
Appendix I Thorn s Three Basic Principles 166
Appendix II The Proof of Thorn s Classification Theorem .... 181
Further Reading 192
Index 197
|
| adam_txt |
CONTENTS
Introduction ix
Acknowledgement xii
Chapter 1 Introduction to Singularity Theory with Historical Remarks . 1
1. Introduction with naive discussion 1
2. Elementary definitions 3
3. Genericity 12
k. Stability 14
5. Singularities 20
Chapter 2 On Singularities of Mappings from the Plane into the Plane . 24
1. Introduction 24
2. Jet spaces 25
3. Transversality 26
It . Morse Lemma the genericity aspect 31
5. Characterization of folds and cusps 33
6. Whitney's Theorem 43
7. The proof of Theorem 6.1 44
8. The proof of Theorem 6.2 48
Chapter 3 Unfoldings of Mappings 52
1. Introduction 52
2. Germs of mappings 55
3. Finitely determined germs 60
1+. Universal unfolding 66
5. Thorn's Classification Theorem 85
Chapter k Catastrophe Theory 95
1. Introduction 95
2. Naive discussion with illustrative examples 96
3. The elementary catastrophes 100
k. Types of elementary catastrophes 10U
Chapter 5 Thorn Whitney Stratification Theory 120
1. Introduction 120
2. Examples 122
3. Regularity conditions of H. Whitney 124
k. Fundamental theorems 132
5. Ratio test 138
viii
CONTENTS
Chapter 6 C Sufficiency of Jets 142
1. Introduction 142
2. Criterion of C° and v sufficiency of jets in Jr(n,l) 147
3. Degree of C° sufficiency 155
k . Sufficiency of jets in Jr(n,p) 161
Appendix I Thorn's Three Basic Principles 166
Appendix II The Proof of Thorn's Classification Theorem . 181
Further Reading 192
Index 197 |
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| spelling | Lu, Yongzhen Verfasser aut Singularity theory and an introduction to catastrophe theory Yung-Chen Lu 2. corr. print. New York, NY [u.a.] Springer c 1976 199 S. Ill. txt rdacontent n rdamedia nc rdacarrier Universitext Applications différentiables ram Catastrophes, Théorie des ram Singularités (mathématiques) ram Variétés (Mathématiques) point singulier inriac théorie catastrophe inriac théorie singularité inriac Differentialtopologie (DE-588)4012255-4 gnd rswk-swf Singularität Mathematik (DE-588)4077459-4 gnd rswk-swf Katastrophentheorie (DE-588)4029930-2 gnd rswk-swf Kataklysmentheorie (DE-588)4227569-6 gnd rswk-swf 1\p (DE-588)4151278-9 Einführung gnd-content Katastrophentheorie (DE-588)4029930-2 s DE-604 Singularität Mathematik (DE-588)4077459-4 s 2\p DE-604 Differentialtopologie (DE-588)4012255-4 s 3\p DE-604 Kataklysmentheorie (DE-588)4227569-6 s 4\p DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015128817&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Lu, Yongzhen Singularity theory and an introduction to catastrophe theory Applications différentiables ram Catastrophes, Théorie des ram Singularités (mathématiques) ram Variétés (Mathématiques) point singulier inriac théorie catastrophe inriac théorie singularité inriac Differentialtopologie (DE-588)4012255-4 gnd Singularität Mathematik (DE-588)4077459-4 gnd Katastrophentheorie (DE-588)4029930-2 gnd Kataklysmentheorie (DE-588)4227569-6 gnd |
| subject_GND | (DE-588)4012255-4 (DE-588)4077459-4 (DE-588)4029930-2 (DE-588)4227569-6 (DE-588)4151278-9 |
| title | Singularity theory and an introduction to catastrophe theory |
| title_auth | Singularity theory and an introduction to catastrophe theory |
| title_exact_search | Singularity theory and an introduction to catastrophe theory |
| title_exact_search_txtP | Singularity theory and an introduction to catastrophe theory |
| title_full | Singularity theory and an introduction to catastrophe theory Yung-Chen Lu |
| title_fullStr | Singularity theory and an introduction to catastrophe theory Yung-Chen Lu |
| title_full_unstemmed | Singularity theory and an introduction to catastrophe theory Yung-Chen Lu |
| title_short | Singularity theory and an introduction to catastrophe theory |
| title_sort | singularity theory and an introduction to catastrophe theory |
| topic | Applications différentiables ram Catastrophes, Théorie des ram Singularités (mathématiques) ram Variétés (Mathématiques) point singulier inriac théorie catastrophe inriac théorie singularité inriac Differentialtopologie (DE-588)4012255-4 gnd Singularität Mathematik (DE-588)4077459-4 gnd Katastrophentheorie (DE-588)4029930-2 gnd Kataklysmentheorie (DE-588)4227569-6 gnd |
| topic_facet | Applications différentiables Catastrophes, Théorie des Singularités (mathématiques) Variétés (Mathématiques) point singulier théorie catastrophe théorie singularité Differentialtopologie Singularität Mathematik Katastrophentheorie Kataklysmentheorie Einführung |
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