PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Czasopismo
1995 | 113 | 3 | 223-248
Tytuł artykułu

Singularities and normal forms of generic 2-distributions on 3-manifolds

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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).
Słowa kluczowe
Twórcy
autor
  • Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-950 Warszawa, Poland
  • Department of Mathematics, Technion, 32000 Haifa, Israel
Bibliografia
  • [A] V. I. Arnold, Mathematical Methods of Classical Mechanics, Springer, New York, 1978.
  • [AI] V. I. Arnold and Yu. S. Il'yashenko, Ordinary Differential Equations, in: Modern Problems in Mathematics, Dynamical Systems 1, Springer, Berlin 1985.
  • [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.
  • [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).
  • [GG] M. Golubitsky and V. Guillemin, Stable Mappings and Their Singularities, Springer, Berlin, 1973.
  • [GT] M. Golubitsky and D. Tischler, On the local stability of differential forms, Trans. Amer. Math. Soc. 223 (1976), 205-221.
  • [JP] B. Jakubczyk and F. Przytycki, Singularities of k-tuples of vector fields, Dissertationes Math. 213 (1984).
  • [L] V. V. Lychagin, Local classification of first order nonlinear partial differential equations, Uspekhi Mat. Nauk 30 (1) (1975), 101-171 (in Russian).
  • [M] J. Martinet, Sur les singularités des formes différentielles, Ann. Inst. Fourier (Grenoble) 20 (1) (1970), 95-178.
  • [MZ] P. Mormul and M. Zhitomirskiĭ, Modules of vector fields, differential forms and degenerations of differential systems, Trans. Amer. Math. Soc., to appear.
  • [P] F. Pelletier, Singularités d'ordre supérieur de 1-formes, 2-formes et équations de Pfaff, Publ. Math. IHES 61 (1985).
  • [R] R. Roussarie, Modules locaux de champs et de formes, Astérisque 30 (1975).
  • [Z1] M. Zhitomirskiĭ, Singularities and normal forms of odd-dimensional Pfaff equations, Funktsional. Anal. i Prilozhen. 23 (1) (1989), 70-71 (in Russian).
  • [Z2] M. Zhitomirskiĭ, Typical Singularities of Differential 1-forms and Pfaffian Equations, Transl. Math. Monographs 113, Amer. Math. Soc., Providence, 1992.
  • [Z3] M. Zhitomirskiĭ, Finitely determined 1-forms ω, $ω_ 0≠0$, are exhausted by Darboux and Martinet models, Funktsional. Anal. i Prilozhen. 19 (1) (1985), 59-61 (in Russian).
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-smv113i3p223bwm
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.