Singularities and normal forms of smooth distributions

M. Zhitomirskiĭ

Banach Center Publications (1995)

  • Volume: 32, Issue: 1, page 395-409
  • ISSN: 0137-6934

Abstract

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In this expository paper we present main results (from classical to recent) on local classification of smooth distributions.

How to cite

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Zhitomirskiĭ, M.. "Singularities and normal forms of smooth distributions." Banach Center Publications 32.1 (1995): 395-409. <http://eudml.org/doc/262684>.

@article{Zhitomirskiĭ1995,
abstract = {In this expository paper we present main results (from classical to recent) on local classification of smooth distributions.},
author = {Zhitomirskiĭ, M.},
journal = {Banach Center Publications},
keywords = {smooth distributions; normal forms; singularities},
language = {eng},
number = {1},
pages = {395-409},
title = {Singularities and normal forms of smooth distributions},
url = {http://eudml.org/doc/262684},
volume = {32},
year = {1995},
}

TY - JOUR
AU - Zhitomirskiĭ, M.
TI - Singularities and normal forms of smooth distributions
JO - Banach Center Publications
PY - 1995
VL - 32
IS - 1
SP - 395
EP - 409
AB - In this expository paper we present main results (from classical to recent) on local classification of smooth distributions.
LA - eng
KW - smooth distributions; normal forms; singularities
UR - http://eudml.org/doc/262684
ER -

References

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  2. R. L. Bryant and L. Hsu, (1993), Rigidity of integral curves of rank 2 distributions, Invent. Math. 114, 435-461. Zbl0807.58007
  3. F. Engel, (1889), Zur Invariantentheorie der Systeme von Pfaffschen Gleichungen, Berichte Verhandl. Königl. Sachsischen Gesell. Wiss. Math.-Phys. Kl. 41. Zbl21.0340.01
  4. E. Goursat, (1923), Leçons sur le Problème de Pfaff, Hermann, Paris. Zbl48.0538.01
  5. B. Jakubczyk and F. Przytycki, (1979), On J. Martinet's conjecture, Bull. Polish Acad. Sci. Math. 27. Zbl0451.58004
  6. B. Jakubczyk and F. Przytycki, (1984), Singularities of k-tuples of vector fields, Dissertationes Math. (Rozprawy Mat.) 213. Zbl0565.58007
  7. 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. Zbl0516.58004
  8. W. Liu and H. J. Sussmann, (1994), Shortest paths for sub-Riemannian metrics of rank-2 distributions, preprint, Rutgers University. 
  9. J. Martinet, (1970), Sur les singularités des formes différentielles, Ann. Inst. Fourier (Grenoble) 20 (1), 95-178. Zbl0189.10001
  10. R. Montgomery, (1995), Abnormal minimizers, SIAM J. Control Optim., to appear. Zbl0816.49019
  11. P. Mormul, (1988), Singularities of triples of vector fields on R 4 : the focusing stratum, Studia Math. 91, 241-273. Zbl0681.58039
  12. 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. Zbl0694.58005
  13. 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). Zbl0780.58004
  14. M. Zhitomirskiĭ, (1988), Singularities and normal forms of even-dimensional Pfaff equations, Russian Math. Surveys 43 (5), 266-267. 
  15. M. Zhitomirskiĭ, (1989), Singularities and normal forms of odd-dimensional Pfaff equations, Functional Anal. Appl. 23 (1), 59-61. 
  16. M. Zhitomirskiĭ, (1990), Normal forms of germs of distributions with a fixed growth vector, Algebra i Anal. 2 (5), 125-149 (in Russian). 
  17. M. Zhitomirskiĭ, (1990a), Normal forms of germs of 2-dimensional distributions on R 4 , Functional Anal. Appl. 24 (2), 150-152. 
  18. M. Zhitomirskiĭ, (1991), Normal forms of germs of smooth distributions, Math. Notes 49 (2), 139-144. Zbl0729.58006
  19. M. Zhitomirskiĭ, (1992), Typical Singularities of Differential 1-Forms and Pfaffian Equations, Transl. Math. Monographs 113, Amer. Math. Soc., Providence, 1992. 

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