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Multi-flag systems and ordinary differential equations

Published online by Cambridge University Press:  22 January 2016

A. Kumpera  and
J. L. Rubin
A. Kumpera
Affiliation:
Universidade Federal do Pará, kumpera@ufpa.br
J. L. Rubin
Affiliation:
Institut du Non-Linéaire de Nice, rubin@inln.cnrs.fr
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Abstract

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We discuss the Monge problem for under-determined systems of ordinary differential equations with an arbitrary degree of freedom and give a sufficient condition, in terms of truncated multi-flag systems, for the Monge property to hold. This condition extends in a natural way the Cartan criterion valid for systems with one degree of freedom.

Keywords

34C2058A1558A1758A30

Information

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 166 , June 2002 , pp. 1 - 27
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2002

References

[1] Cartan, E., Sur quelques quadratures dont l’élément différentiel contient des fonctions arbitraires, Bull. Soc. Math. France, 29 (1901), 118–130, Oeuvres Complétes, Part. II, Vol. 2.Google Scholar
[2] Cartan, E., Les systémes de Pfaff à cinq variables et les équations aux dérivées par tielles du second ordre, Ann. Sci. Ec. Normale Sup., 27 (1910), 109–192, Oeuvres Complétes, Part. II, Vol. 2.Google Scholar
[3] Cartan, E., Sur l’équivalence absolue de certains systémes d’équations différentielles et sur certaines familles de courbes, Bull. Soc. Math. France, 42 (1914), 12–48, Oeuvres Complétes, Part. II, Vol. 2.Google Scholar
[4] Cartan, E., Sur l’intégration de certains systémes indéterminés d’équations différen tielles, J. reine angew. Math., 145 (1915), 86–91, Oeuvres Complétes, Part. II, Vol. 2.Google Scholar
[5] Cheaito, M. and Mormul, P., Rank-2 distributions satisfying the Goursat condition: all their local models in dimension 7 and 8, ESAIM: Control, Optimisation and Calculus of Variations, 4 (1999), 137–158.Google Scholar
[6] Engel, F., Zur Invariantentheorie der Systeme von Pfaff’schen Gleichungen, Math.-Phys., 41 (1889), 157–176.Google Scholar
[7] Goursat, E., Sur le probléme de Monge, Bull. Soc. Math. France, 33 (1905), 201–216.Google Scholar
[8] Goursat, E., Lec¸ons sur le Probléme de Pfaff, Hermann, Paris, 1922.Google Scholar
[9] Kumpera, A., Equivalence locale des structures de contact de codimension un, Canad. J. Math., 22 (1970), 1123–1128.Google Scholar
[10] Kumpera, A., On the Lie and Cartan theory of invariant differential systems, J. Math. Sci. Univ. Tokyo, 6 (1999), 229–314.Google Scholar
[11] Kumpera, A., Toulouse Lectures, may 1998.Google Scholar
[12] Kumpera, A., Flag systems and ordinary differential equations, Annali Mat. Pura ed Appl., 177 (1999), 315–329.Google Scholar
[13] Kumpera, A. and Ruiz, C., Sur l’équivalence locale des systémes de Pfaff en drapeau, in: “Monge-Ampére equations and related topics (F.Gherardelli, Ed.)”, Ist. Alta Mat., Roma, 1982, p. 201–248.Google Scholar
[14] Kumpera, R., Sur la géométrie de contact d’ordre supérieur, Portugal. Math., 44 (1987), 199–212.Google Scholar
[15] Martinet, J., Classes caractéristiques des systémes de Pfaff, Lect. Notes in Math., Vol. 392, Springer-Verlag, Berlin, 1974, p. 30–37.Google Scholar
[16] Monge, G., Oeuvre, Gauthier-Villars, Paris, 1821.Google Scholar
[17] Mormul, P., Contact Hamiltonians distinguishing locally certain Goursat systems, in: “Poisson Geometry”, Banach Centre Publications, 51, Polish Acad. Sci., Warsaw, 2000, 219–230.Google Scholar
[18] Weber, E. von, Zur Invariantentheorie der Systeme Pfaff’scher Gleichungen, Berichte Ges. Leipzig, Math.-Phys., 50 (1898), 207–229.Google Scholar
[19] Zervos, P., Sur l’intégration de certains systémes indéterminés d’équations différentielles, Journal de Crelle (J. reine angew. Math.), 143 (1913), 300–312.CrossRefGoogle Scholar