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Liczba wyników
1995 | 32 | 1 | 395-409

Tytuł artykułu

Singularities and normal forms of smooth distributions

Treść / Zawartość

Języki publikacji

EN

Abstrakty

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

Rocznik

Tom

32

Numer

1

Strony

395-409

Daty

wydano
1995

Twórcy

  • Department of Mathematics, Technion, 32000 Haifa, Israel

Bibliografia

  • R. L. Bryant, (1994), Smooth normal form for generic germs of 2-distributions on 5-manifolds, a letter to the author.
  • R. L. Bryant and L. Hsu, (1993), Rigidity of integral curves of rank 2 distributions, Invent. Math. 114, 435-461.
  • F. Engel, (1889), Zur Invariantentheorie der Systeme von Pfaffschen Gleichungen, Berichte Verhandl. Königl. Sachsischen Gesell. Wiss. Math.-Phys. Kl. 41.
  • E. Goursat, (1923), Leçons sur le Problème de Pfaff, Hermann, Paris.
  • B. Jakubczyk and F. Przytycki, (1979), On J. Martinet's conjecture, Bull. Polish Acad. Sci. Math. 27.
  • B. Jakubczyk and F. Przytycki, (1984), Singularities of k-tuples of vector fields, Dissertationes Math. (Rozprawy Mat.) 213.
  • 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.
  • W. Liu and H. J. Sussmann, (1994), Shortest paths for sub-Riemannian metrics of rank-2 distributions, preprint, Rutgers University.
  • J. Martinet, (1970), Sur les singularités des formes différentielles, Ann. Inst. Fourier (Grenoble) 20 (1), 95-178.
  • R. Montgomery, (1995), Abnormal minimizers, SIAM J. Control Optim., to appear.
  • P. Mormul, (1988), Singularities of triples of vector fields on $R^4$: the focusing stratum, Studia Math. 91, 241-273.
  • 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.
  • 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).
  • M. Zhitomirskiĭ, (1988), Singularities and normal forms of even-dimensional Pfaff equations, Russian Math. Surveys 43 (5), 266-267.
  • M. Zhitomirskiĭ, (1989), Singularities and normal forms of odd-dimensional Pfaff equations, Functional Anal. Appl. 23 (1), 59-61.
  • M. Zhitomirskiĭ, (1990), Normal forms of germs of distributions with a fixed growth vector, Algebra i Anal. 2 (5), 125-149 (in Russian).
  • M. Zhitomirskiĭ, (1990a), Normal forms of germs of 2-dimensional distributions on $R^4$, Functional Anal. Appl. 24 (2), 150-152.
  • M. Zhitomirskiĭ, (1991), Normal forms of germs of smooth distributions, Math. Notes 49 (2), 139-144.
  • 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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