Typical singularities of differential 1-forms and Pfaffian equations (Translations of Mathematical Monographs)

Cover......Page 1
Title Page......Page 4
Copyright Page......Page 5
Dedication......Page 6
Contents......Page 8
Introduction......Page 10
1. Stable and finitely determined germs; normal forms......Page 14
2. Geometry of singularities......Page 18
3. Differential 1-forms and Pfaffian equations......Page 22
4. Singularities and their characteristics......Page 27
5. The homotopy method and its modifications......Page 30
6. The infinitesimal equation, functional moduli, and "wild" jets......Page 33
7. Classsification of submanifolds of a contact manifold......Page 38
8. Solvability of equations with respect to germs of flat functions......Page 39
9. Commentary......Page 41
10. The class of a germ; preliminary normal form; Darboux theorem......Page 44
11. Singularities and their adjacencies......Page 48
12. Classification of coclass 1 singularities......Page 54
13. Classification of point singularities......Page 60
14. Basic results and corollaries; tables of singularities; list of normal forms; examples......Page 66
15. Commentary......Page 70
16. Class of Pfaffian equations; classification of 1 -jets; preliminary normal form......Page 72
17. Singularities......Page 74
18. Classification of germs at points of second degeneration manifolds......Page 84
19. Point singularities of 3-dimensional Pfaffian equations......Page 95
20. Degenerations of codimension > 4......Page 104
21. Point singularities of Pfaffian equations in R^{2k+1}......Page 112
22. Basic results and corollaries; table of singularities; list of normal forms; examples......Page 126
23. Commentary......Page 129
24. Singularities associated with the decrease of germ class; preliminary normal form......Page 132
25. Other singularities (of the class n - 3 }......Page 133
26. Classification of first occurring singularities of Pfaffian equations in R', n = 2k > 6......Page 141
27. Degenerations of codimension > 4......Page 150
28. Normal forms of Pfaffian equations in R4......Page 153
30. Basic results and corollaries; table of singularities; list of normal forms......Page 160
31. Commentary......Page 161
Appendix A. Local Classification of First-Order Partial Differential Equations......Page 166
Appendix B. Classification of Submanifolds of a Contact Manifold......Page 168
Appendix C. Feedback Equivalence of Control Systems......Page 170
Appendix D. Analytic Classification of Differential Forms and Pfaffian Equations......Page 172
Appendix E. Distributions and Differential Systems......Page 175
Appendix F. Topological Classification of Distributions......Page 177
Appendix G. Degenerations of Closed 2-Forms in R^{2k}......Page 178
References......Page 180
Author Index......Page 184
Subject Index......Page 186
List of Symbols......Page 188