In this expository paper we present main results (from classical to recent) on local classification of smooth distributions.
@article{bwmeta1.element.bwnjournal-article-bcpv32z1p395bwm, author = {Zhitomirski\u\i , M.}, title = {Singularities and normal forms of smooth distributions}, journal = {Banach Center Publications}, volume = {31}, year = {1995}, pages = {395-409}, zbl = {0841.58005}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-bcpv32z1p395bwm} }
Zhitomirskiĭ, M. Singularities and normal forms of smooth distributions. Banach Center Publications, Tome 31 (1995) pp. 395-409. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv32z1p395bwm/
[000] R. L. Bryant, (1994), Smooth normal form for generic germs of 2-distributions on 5-manifolds, a letter to the author.
[001] R. L. Bryant and L. Hsu, (1993), Rigidity of integral curves of rank 2 distributions, Invent. Math. 114, 435-461. | Zbl 0807.58007
[002] F. Engel, (1889), Zur Invariantentheorie der Systeme von Pfaffschen Gleichungen, Berichte Verhandl. Königl. Sachsischen Gesell. Wiss. Math.-Phys. Kl. 41. | Zbl 21.0340.01
[003] E. Goursat, (1923), Leçons sur le Problème de Pfaff, Hermann, Paris. | Zbl 48.0538.01
[004] B. Jakubczyk and F. Przytycki, (1979), On J. Martinet's conjecture, Bull. Polish Acad. Sci. Math. 27. | Zbl 0451.58004
[005] B. Jakubczyk and F. Przytycki, (1984), Singularities of k-tuples of vector fields, Dissertationes Math. (Rozprawy Mat.) 213. | Zbl 0565.58007
[006] A. Kumpera and C. Ruiz, (1982), Sur l'équivalence locale des systèmes de Pfaff en drapeau, in: Monge-Ampère Equations and Related Topics, Inst. Alta Mat., Rome, 201-248. | Zbl 0516.58004
[007] W. Liu and H. J. Sussmann, (1994), Shortest paths for sub-Riemannian metrics of rank-2 distributions, preprint, Rutgers University.
[008] J. Martinet, (1970), Sur les singularités des formes différentielles, Ann. Inst. Fourier (Grenoble) 20 (1), 95-178. | Zbl 0189.10001
[009] R. Montgomery, (1995), Abnormal minimizers, SIAM J. Control Optim., to appear. | Zbl 0816.49019
[010] P. Mormul, (1988), Singularities of triples of vector fields on : the focusing stratum, Studia Math. 91, 241-273. | Zbl 0681.58039
[011] A. M. Vershik and V. Ya. Gershkovich, (1988), An estimate of the functional dimension for the space of orbits of germs of generic distributions, Math. Notes 44 (5), 806-810. | Zbl 0694.58005
[012] A. M. Vershik and V. Ya. Gershkovich, (1989), A bundle of nilpotent Lie algebras over a nonholomorphic manifold (nilpotentization), Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. 172 (10), 21-40 (in Russian). | Zbl 0780.58004
[013] M. Zhitomirskiĭ, (1988), Singularities and normal forms of even-dimensional Pfaff equations, Russian Math. Surveys 43 (5), 266-267.
[014] M. Zhitomirskiĭ, (1989), Singularities and normal forms of odd-dimensional Pfaff equations, Functional Anal. Appl. 23 (1), 59-61.
[015] M. Zhitomirskiĭ, (1990), Normal forms of germs of distributions with a fixed growth vector, Algebra i Anal. 2 (5), 125-149 (in Russian).
[016] M. Zhitomirskiĭ, (1990a), Normal forms of germs of 2-dimensional distributions on , Functional Anal. Appl. 24 (2), 150-152.
[017] M. Zhitomirskiĭ, (1991), Normal forms of germs of smooth distributions, Math. Notes 49 (2), 139-144. | Zbl 0729.58006
[018] M. Zhitomirskiĭ, (1992), Typical Singularities of Differential 1-Forms and Pfaffian Equations, Transl. Math. Monographs 113, Amer. Math. Soc., Providence, 1992.