Geodesic
$\Cal D$-modules, contact valued calculus and Poincaré-Cartan form
Czechoslovak Mathematical Journal, Tome 49 (1999) no. 3, pp. 585-606 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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Classification : 58A20, 58E30, 58J10 
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}
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Blanco, Ricardo J. Alonso. $\Cal D$-modules, contact valued calculus and Poincaré-Cartan form. Czechoslovak Mathematical Journal, Tome 49 (1999) no. 3, pp. 585-606. http://geodesic.mathdoc.fr/item/CMJ_1999_49_3_a10/

[1] P.L. García: The Poincaré-Cartan invariant in the calculus of variations. Symp. Math. XIV (1974), 219–246. | MR

[2] P.L. García and J. Muñoz: On the geometrical structure of higher order variational calculus. Proceedings of the IUTAM-ISIMM. Symposium on Modern Developments in Analytical Mechanics (Bologna), Tecnoprint, 1983, pp. 127–147. | MR

[3] H. Goldschmidt and S. Sternberg: The Hamilton-Cartan formalism in the calculus of variations. Ann. Inst. Fourier (Grenoble) 23 (1973), 203–267. | DOI | MR

[4] M. Gotay: An exterior differential system approach to the Cartan form. Géométrie Symplectique et Physique Mathématique (Boston), P. Donato et al., Boston, 1991, pp. 160–188. | MR

[5] H. Hess: Symplectic connections in geometric quantization and factor orderings. Ph.D. thesis, Berlin, 1981, pp. .

[6] M. Horác and I. Kolá: On the higher order Poincaré-Cartan forms. Czechoslovak Math. J. 33 (1983), 467–475. | MR

[7] I. Kolá: A geometric version of the higher order Hamilton formalism in fibered manifolds. J. Geom. Phys. 1 (1984), 127–137. | DOI | MR

[8] I. Kolá, P. Michor and J. Slovak: Natural Operations in Differential Geometry. Springer-Verlag, Berlin, 1993, pp. . | MR

[9] D. Krupka: A geometric theory of ordinary first order variational problems in fibered manifolds I. Critical sections. J. Math. Anal. Appl. 49 (1975), 180–206. | DOI | MR | Zbl

[10] A. Kumpera: Invariants différentiels d’un pseudogroupe de Lie, I. J. Differential Geom. 10 (1975), 289–345. | DOI | MR | Zbl

[11] B. Kupershmidt: Geometry of jet bundles and the structure of Lagrangian and Hamiltonian formalism. Lect. Notes in Math. 775, 1980, pp. 162–217. | MR

[12] J. Muñoz: Poincaré-Cartan forms in higher order variational calculus on fibred manifolds. Rev. Mat. Iberoamericana 1 (1985), no. 4, 85–126. | DOI | MR

[13] P.J. Olver: Equivalence and the Cartan form. Acta Appl. Math. 31 (1993), 99–136. | DOI | MR | Zbl

[14] J. Rodríguez: Sobre los espacios de jets y los fundamentos de la teoría de los sistemas de ecuaciones en derivadas parciales. Ph.D. thesis, Salamanca, 1990.

[15] C. Ruiz: Prolongament formel des systemes differentiels exterieurs d’ordre superieur. C. R. Acad. Sci. Paris Sér. I Math. 285 (1977), 1077–1080. | MR

[16] D. Saunders: An alternative approach to the Cartan form in Lagrangian field theories. J. Phys. A 20 (1987), 339–349. | DOI | MR | Zbl

[17] D. Saunders: The Geometry of Jet Bundles. Lecture Notes Series, vol. 142, London Mathematical Society, Cambridge University Press, New York, 1989, pp. . | MR | Zbl

[18] J.P. Schneiders: An introduction to the D-Modules. Bull. Soc. Roy. Sci. Liège 63 (1994), 223–295. | MR

[19] W.M. Tulczyjew: The Euler-Lagrange resolution. Lect. Notes in Math. 836, 1980, pp. 22–48. | MR | Zbl

[20] A. Weil: Théorie des points proches sur les variétés différentiables. Colloque de Géometrie Différentielle, C.N.R.S. (1953), 111–117. | MR | Zbl