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Trudy Mat. Inst. Steklova, 2002, Volume 236, Pages 491–502 (Mi tm318)  

This article is cited in 1 scientific paper (total in 1 paper)

Discrete Models of Codimension-Two Singularities of Goursat Flags of Arbitrary Length with One Flag's Member in Singular Position

P. Mormul

Institute of Mathematics, Warsaw University

Abstract: Generic germs of Goursat distributions (special subbundles in tangent bundles having the flag of consecutive Lie squares of ranks growing always by 1) were classified a century ago by von Weber; his discrete models are the chained systems that are well known in control theory. Germs of codimension 1, for Goursat distributions of all coranks, were classified by us in 1999. These singularities are simple as well. Singularities of codimension 2 of Goursat flags of arbitrary corank split into two geometrically distinct classes. In this paper we show that one of these classes consists of simple germs, and give a list of discrete models for them. This is in contrast with the fact that in the second class there do exist singularities of modality at least two.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2002, 236, 478–489

Bibliographic databases:
UDC: 517.9
Received in June 2001
Language:

Citation: P. Mormul, “Discrete Models of Codimension-Two Singularities of Goursat Flags of Arbitrary Length with One Flag's Member in Singular Position”, Differential equations and dynamical systems, Collected papers. Dedicated to the 80th anniversary of academician Evgenii Frolovich Mishchenko, Trudy Mat. Inst. Steklova, 236, Nauka, MAIK Nauka/Inteperiodika, M., 2002, 491–502; Proc. Steklov Inst. Math., 236 (2002), 478–489

Citation in format AMSBIB
\Bibitem{Mor02}
\by P.~Mormul
\paper Discrete Models of Codimension-Two Singularities of Goursat Flags
of Arbitrary Length with One Flag's Member in Singular Position
\inbook Differential equations and dynamical systems
\bookinfo Collected papers. Dedicated to the 80th anniversary of academician Evgenii Frolovich Mishchenko
\serial Trudy Mat. Inst. Steklova
\yr 2002
\vol 236
\pages 491--502
\publ Nauka, MAIK Nauka/Inteperiodika
\publaddr M.
\mathnet{http://mi.mathnet.ru/tm318}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1931048}
\zmath{https://zbmath.org/?q=an:1022.58018}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2002
\vol 236
\pages 478--489


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    This publication is cited in the following articles:
    1. Montgomery R., Zhitomirskii M., “Points and Curves in the Monster Tower”, Memoirs of the American Mathematical Society, 203:956 (2010), 1  crossref  mathscinet  isi  scopus
  •    . . .  Proceedings of the Steklov Institute of Mathematics
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