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ArticleOriginal scientific text

Title

Singularities and normal forms of smooth distributions

Authors 1

Affiliations

  1. Department of Mathematics, Technion, 32000 Haifa, Israel

Abstract

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

Bibliography

  1. R. L. Bryant, (1994), Smooth normal form for generic germs of 2-distributions on 5-manifolds, a letter to the author.
  2. R. L. Bryant and L. Hsu, (1993), Rigidity of integral curves of rank 2 distributions, Invent. Math. 114, 435-461.
  3. F. Engel, (1889), Zur Invariantentheorie der Systeme von Pfaffschen Gleichungen, Berichte Verhandl. Königl. Sachsischen Gesell. Wiss. Math.-Phys. Kl. 41.
  4. E. Goursat, (1923), Leçons sur le Problème de Pfaff, Hermann, Paris.
  5. B. Jakubczyk and F. Przytycki, (1979), On J. Martinet's conjecture, Bull. Polish Acad. Sci. Math. 27.
  6. B. Jakubczyk and F. Przytycki, (1984), Singularities of k-tuples of vector fields, Dissertationes Math. (Rozprawy Mat.) 213.
  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.
  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.
  10. R. Montgomery, (1995), Abnormal minimizers, SIAM J. Control Optim., to appear.
  11. P. Mormul, (1988), Singularities of triples of vector fields on R4: the focusing stratum, Studia Math. 91, 241-273.
  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.
  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).
  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 R4, Functional Anal. Appl. 24 (2), 150-152.
  18. M. Zhitomirskiĭ, (1991), Normal forms of germs of smooth distributions, Math. Notes 49 (2), 139-144.
  19. M. Zhitomirskiĭ, (1992), Typical Singularities of Differential 1-Forms and Pfaffian Equations, Transl. Math. Monographs 113, Amer. Math. Soc., Providence, 1992.
Banach Center Publications
1995/32/1
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Pages:
395-409
Main language of publication
English
Published
1995
Exact and natural sciences