On implicit Lagrangian differential systems
Janeczko, S.
Annales Polonici Mathematici, Tome 75 (2000), p. 133-141 / Harvested from The Polish Digital Mathematics Library

Let (P,ω) be a symplectic manifold. We find an integrability condition for an implicit differential system D' which is formed by a Lagrangian submanifold in the canonical symplectic tangent bundle (TP,ὡ).

Publié le : 2000-01-01
EUDML-ID : urn:eudml:doc:208361
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     title = {On implicit Lagrangian differential systems},
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     volume = {75},
     year = {2000},
     pages = {133-141},
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Janeczko, S. On implicit Lagrangian differential systems. Annales Polonici Mathematici, Tome 75 (2000) pp. 133-141. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv74z1p133bwm/

[000] [1] V. I. Arnold, S. M. Gusein-Zade and A. N. Varchenko, Singularities of Differentiable Maps, Vol. 1, Birkhäuser, Boston, 1985. | Zbl 1297.32001

[001] [2] J. W. Bruce, A note on first order differential equations of degree greater than one and wavefront evolution, Bull. London Math. Soc. 16 (1984), 139-144. | Zbl 0503.34003

[002] [3] I. Ekeland, Discontinuités de champs hamiltoniens et existence de solutions optimales en calcul des variations, Publ. Math. I.H.E.S. 47 (1977), 5-32. | Zbl 0447.49015

[003] [4] S. Janeczko, Systems of rays in the presence of distribution of hyperplanes, in: Banach Center Publ. 32, Inst. Math., Polish Acad. Sci., 1995, 245-260. | Zbl 0844.57030

[004] [5] S. Janeczko, Hamiltonian geodesics in nonholonomic differential systems, Reports Math. Phys. 40 (1997), 217-224. | Zbl 0911.58003

[005] [6] S. Janeczko, On isotropic submanifolds and evolution of quasicaustics, Pacific J. Math. 158 (1993), 317-334. | Zbl 0806.58023

[006] [7] J. Kijowski and W. M. Tulczyjew, A Symplectic Framework for Field Theories, Lecture Notes in Physics 107, Springer, 1979. | Zbl 0439.58002

[007] [8] J. Martinet, Singularities of Smooth Functions and Maps, Cambridge Univ. Press, Cambridge, 1982.

[008] [9] J. N. Mather, Solutions of generic linear equations, in: Dynamical Systems (Salvador, 1971), Academic Press, 1973, 185-193.

[009] [10] R. Montgomery, A survey of singular curves in sub-Riemannian geometry, J. Dynam. Control Systems 1 (1995), 49-90. | Zbl 0941.53021

[010] [11] J. Śniatycki and W. M. Tulczyjew, Generating forms of Lagrangian submanifolds, Indiana Univ. Math. J. 22 (1972), 267-275. | Zbl 0237.58002

[011] [12] F. Takens, Implicit differential equations: some open problems, in: Lecture Notes in Math. 535, Springer, 1976, 237-253.

[012] [13] R. Thom, Sur les équations différentielles multiformes et leurs intégrales singulières, Bol. Soc. Brasil. Mat. 3 (1972), 1-11. | Zbl 0396.34018

[013] [14] A. Weinstein, Lectures on Symplectic Manifolds, CBMS Regional Conf. Ser. in Math. 29, Amer. Math. Soc., Providence, RI, 1977.