Typical singularities of differential 1-forms and Pfaffian equations
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| Sprache: | English |
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Providence, RI
American Math. Society u.a.
1992
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| Schriftenreihe: | Translations of mathematical monographs
113 |
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| 100 | 1 | |a Žitomirskij, Michail J. |e Verfasser |4 aut | |
| 240 | 1 | 0 | |a Tipičnye osobennosti differencial'nych 1-form i uravnenij Pfaffa |
| 245 | 1 | 0 | |a Typical singularities of differential 1-forms and Pfaffian equations |c Michail Zhitomirskii |
| 264 | 1 | |a Providence, RI |b American Math. Society u.a. |c 1992 | |
| 300 | |a XI, 176 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 1 | |a Translations of mathematical monographs |v 113 | |
| 500 | |a Aus d. Russ. übers. | ||
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Datensatz im Suchindex
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|---|---|
| adam_text | Contents
Introduction ix
Chapter I. Main Results 1
§ 1. Stable and finitely determined germs; normal forms 1
§2. Geometry of singularities 5
Chapter II. Basic Notions, Definitions, Notation, and Constructions 9
§3. Differential 1 forms and Pfaffian equations 9
§4. Singularities and their characteristics 14
§5. The homotopy method and its modifications 17
§6. The infinitesimal equation, functional moduli, and wild jets 20
§7. Classsification of submanifolds of a contact manifold 25
§8. Solvability of equations with respect to germs of flat functions 26
§9. Commentary 28
Chapter III. Classification of Germs of Differential Forms 31
§10. The class of a germ; preliminary normal form; Darboux
theorem 31
§11. Singularities and their adjacencies 35
§12. Classification of coclass 1 singularities 41
§13. Classification of point singularities 47
§14. Basic results and corollaries; tables of singularities; list of
normal forms; examples 53
§15. Commentary 57
Chapter IV. Classification of Germs of Odd Dimensional Pfafnan
Equations 59
§16. Class of Pfafnan equations; classification of 1 jets; preliminary
normal form 59
§17. Singularities 61
§18. Classification of germs at points of second degeneration
manifolds 71
§19. Point singularities of 3 dimensional Pfaffian equations 82
§20. Degenerations of codimension 4 91
§21. Point singularities of Pfafnan equations in R2k+l 99
vii
viii CONTENTS
§22. Basic results and corollaries; table of singularities; list of
normal forms; examples 113
§23. Commentary 116
Chapter V. Classification of Germs of Even Dimensional Pfaffian
Equations 119
§24. Singularities associated with the decrease of germ class;
preliminary normal form 119
§25. Other singularities (of the class n 3 ) 120
§26. Classification of first occurring singularities of Pfaffian
equations in Rn , n = 2k 6 128
§27. Degenerations of codimension 4 137
§28. Normal forms of Pfaffian equations in R4 140
§29. Point singularities 147
§30. Basic results and corollaries; table of singularities; list of
normal forms 147
§31. Commentary 148
Appendix A. Local Classification of First Order Partial Differential
Equations 153
Appendix B. Classification of Submanifolds of a Contact Manifold 155
Appendix C. Feedback Equivalence of Control Systems 157
Appendix D. Analytic Classification of Differential Forms and Pfaffian
Equations 159
Appendix E. Distributions and Differential Systems 162
Appendix F. Topological Classification of Distributions 164
Ik
Appendix G. Degenerations of Closed 2 Forms in R 165
References 167
Author Index 171
Subject Index 173
List of Symbols 175
|
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| author_facet | Žitomirskij, Michail J. |
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| bvnumber | BV007193403 |
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| id | DE-604.BV007193403 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T16:57:23Z |
| institution | BVB |
| isbn | 0821845675 |
| language | English |
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| physical | XI, 176 S. |
| publishDate | 1992 |
| publishDateSearch | 1992 |
| publishDateSort | 1992 |
| publisher | American Math. Society u.a. |
| record_format | marc |
| series | Translations of mathematical monographs |
| series2 | Translations of mathematical monographs |
| spelling | Žitomirskij, Michail J. Verfasser aut Tipičnye osobennosti differencial'nych 1-form i uravnenij Pfaffa Typical singularities of differential 1-forms and Pfaffian equations Michail Zhitomirskii Providence, RI American Math. Society u.a. 1992 XI, 176 S. txt rdacontent n rdamedia nc rdacarrier Translations of mathematical monographs 113 Aus d. Russ. übers. Differentialform (DE-588)4149772-7 gnd rswk-swf Pfaff-Gleichung (DE-588)4319093-5 gnd rswk-swf Singularität Mathematik (DE-588)4077459-4 gnd rswk-swf Differentialform (DE-588)4149772-7 s Singularität Mathematik (DE-588)4077459-4 s DE-604 Pfaff-Gleichung (DE-588)4319093-5 s Translations of mathematical monographs 113 (DE-604)BV000002394 113 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004601383&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Žitomirskij, Michail J. Typical singularities of differential 1-forms and Pfaffian equations Translations of mathematical monographs Differentialform (DE-588)4149772-7 gnd Pfaff-Gleichung (DE-588)4319093-5 gnd Singularität Mathematik (DE-588)4077459-4 gnd |
| subject_GND | (DE-588)4149772-7 (DE-588)4319093-5 (DE-588)4077459-4 |
| title | Typical singularities of differential 1-forms and Pfaffian equations |
| title_alt | Tipičnye osobennosti differencial'nych 1-form i uravnenij Pfaffa |
| title_auth | Typical singularities of differential 1-forms and Pfaffian equations |
| title_exact_search | Typical singularities of differential 1-forms and Pfaffian equations |
| title_full | Typical singularities of differential 1-forms and Pfaffian equations Michail Zhitomirskii |
| title_fullStr | Typical singularities of differential 1-forms and Pfaffian equations Michail Zhitomirskii |
| title_full_unstemmed | Typical singularities of differential 1-forms and Pfaffian equations Michail Zhitomirskii |
| title_short | Typical singularities of differential 1-forms and Pfaffian equations |
| title_sort | typical singularities of differential 1 forms and pfaffian equations |
| topic | Differentialform (DE-588)4149772-7 gnd Pfaff-Gleichung (DE-588)4319093-5 gnd Singularität Mathematik (DE-588)4077459-4 gnd |
| topic_facet | Differentialform Pfaff-Gleichung Singularität Mathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004601383&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000002394 |
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