We give a complete classification of germs of generic 2-distributions on 3-manifolds. By a 2-distribution we mean either a module generated by two vector fields (at singular points its dimension decreases) or a Pfaff equation, i.e. a module generated by a differential 1-form (at singular points the dimension of its kernel increases).
@article{bwmeta1.element.bwnjournal-article-smv113i3p223bwm, author = {B. Jakubczyk and M. Zhitomirski\u\i }, title = {Singularities and normal forms of generic 2-distributions on 3-manifolds}, journal = {Studia Mathematica}, volume = {113}, year = {1995}, pages = {223-248}, zbl = {0829.58007}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv113i3p223bwm} }
Jakubczyk, B.; Zhitomirskiĭ, M. Singularities and normal forms of generic 2-distributions on 3-manifolds. Studia Mathematica, Tome 113 (1995) pp. 223-248. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv113i3p223bwm/
[00000] [A] V. I. Arnold, Mathematical Methods of Classical Mechanics, Springer, New York, 1978. | Zbl 0386.70001
[00001] [AI] V. I. Arnold and Yu. S. Il'yashenko, Ordinary Differential Equations, in: Modern Problems in Mathematics, Dynamical Systems 1, Springer, Berlin 1985.
[00002] [AVG] V. I. Arnold, A. N. Varchenko and S. M. Gusein-Zade, Singularities of Differentiable Maps, Vol. 1, Nauka, Moscow, 1982 (in Russian); English transl.: Birkhäuser, 1985.
[00003] [B] G. R. Belitskiĭ, Smooth equivalence of germs of vector fields with one zero eigenvalue or a pair of purely imaginary eigenvalues, Funktsional. Anal. i Prilozhen. 20 (4) (1986), 1-8 (in Russian). | Zbl 0657.58027
[00004] [GG] M. Golubitsky and V. Guillemin, Stable Mappings and Their Singularities, Springer, Berlin, 1973. | Zbl 0294.58004
[00005] [GT] M. Golubitsky and D. Tischler, On the local stability of differential forms, Trans. Amer. Math. Soc. 223 (1976), 205-221. | Zbl 0339.58003
[00006] [JP] B. Jakubczyk and F. Przytycki, Singularities of k-tuples of vector fields, Dissertationes Math. 213 (1984). | Zbl 0565.58007
[00007] [L] V. V. Lychagin, Local classification of first order nonlinear partial differential equations, Uspekhi Mat. Nauk 30 (1) (1975), 101-171 (in Russian).
[00008] [M] J. Martinet, Sur les singularités des formes différentielles, Ann. Inst. Fourier (Grenoble) 20 (1) (1970), 95-178. | Zbl 0189.10001
[00009] [MZ] P. Mormul and M. Zhitomirskiĭ, Modules of vector fields, differential forms and degenerations of differential systems, Trans. Amer. Math. Soc., to appear. | Zbl 0866.58003
[00010] [P] F. Pelletier, Singularités d'ordre supérieur de 1-formes, 2-formes et équations de Pfaff, Publ. Math. IHES 61 (1985). | Zbl 0568.58001
[00011] [R] R. Roussarie, Modules locaux de champs et de formes, Astérisque 30 (1975). | Zbl 0327.57017
[00012] [Z1] M. Zhitomirskiĭ, Singularities and normal forms of odd-dimensional Pfaff equations, Funktsional. Anal. i Prilozhen. 23 (1) (1989), 70-71 (in Russian).
[00013] [Z2] M. Zhitomirskiĭ, Typical Singularities of Differential 1-forms and Pfaffian Equations, Transl. Math. Monographs 113, Amer. Math. Soc., Providence, 1992.
[00014] [Z3] M. Zhitomirskiĭ, Finitely determined 1-forms ω, , are exhausted by Darboux and Martinet models, Funktsional. Anal. i Prilozhen. 19 (1) (1985), 59-61 (in Russian).