| Title:
|
$\Cal D$-modules, contact valued calculus and Poincaré-Cartan form (English) |
| Author:
|
Blanco, Ricardo J. Alonso |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
49 |
| Issue:
|
3 |
| Year:
|
1999 |
| Pages:
|
585-606 |
| . |
| Category:
|
math |
| . |
| MSC:
|
58A20 |
| MSC:
|
58E30 |
| MSC:
|
58J10 |
| idZBL:
|
Zbl 1011.58011 |
| idMR:
|
MR1708350 |
| . |
| Date available:
|
2009-09-24T10:25:39Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127512 |
| . |
| Reference:
|
[1] P.L. García: The Poincaré-Cartan invariant in the calculus of variations.Symp. Math. XIV (1974), 219–246. MR 0406246 |
| Reference:
|
[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 0773483 |
| Reference:
|
[3] H. Goldschmidt and S. Sternberg: The Hamilton-Cartan formalism in the calculus of variations.Ann. Inst. Fourier (Grenoble) 23 (1973), 203–267. MR 0341531, 10.5802/aif.451 |
| Reference:
|
[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 1156539 |
| Reference:
|
[5] H. Hess: Symplectic connections in geometric quantization and factor orderings.Ph.D. thesis, Berlin, 1981, pp. . |
| Reference:
|
[6] M. Horác and I. Kolá: On the higher order Poincaré-Cartan forms.Czechoslovak Math. J. 33 (1983), 467–475. MR 0718929 |
| Reference:
|
[7] I. Kolá: A geometric version of the higher order Hamilton formalism in fibered manifolds.J. Geom. Phys. 1 (1984), 127–137. MR 0794983, 10.1016/0393-0440(84)90007-X |
| Reference:
|
[8] I. Kolá, P. Michor and J. Slovak: Natural Operations in Differential Geometry.Springer-Verlag, Berlin, 1993, pp. . MR 1202431 |
| Reference:
|
[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. Zbl 0312.58002, MR 0362397, 10.1016/0022-247X(75)90169-9 |
| Reference:
|
[10] A. Kumpera: Invariants différentiels d’un pseudogroupe de Lie, I.J. Differential Geom. 10 (1975), 289–345. Zbl 0319.58018, MR 0407911, 10.4310/jdg/1214432795 |
| Reference:
|
[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 0569303 |
| Reference:
|
[12] J. Muñoz: Poincaré-Cartan forms in higher order variational calculus on fibred manifolds.Rev. Mat. Iberoamericana 1 (1985), no. 4, 85–126. MR 0850411, 10.4171/RMI/20 |
| Reference:
|
[13] P.J. Olver: Equivalence and the Cartan form.Acta Appl. Math. 31 (1993), 99–136. Zbl 0794.49041, MR 1223167, 10.1007/BF00990539 |
| Reference:
|
[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. |
| Reference:
|
[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 0515877 |
| Reference:
|
[16] D. Saunders: An alternative approach to the Cartan form in Lagrangian field theories.J. Phys. A 20 (1987), 339–349. Zbl 0652.58002, MR 0874255, 10.1088/0305-4470/20/2/019 |
| Reference:
|
[17] D. Saunders: The Geometry of Jet Bundles.Lecture Notes Series, vol. 142, London Mathematical Society, Cambridge University Press, New York, 1989, pp. . Zbl 0665.58002, MR 0989588 |
| Reference:
|
[18] J.P. Schneiders: An introduction to the D-Modules.Bull. Soc. Roy. Sci. Liège 63 (1994), 223–295. MR 1282516 |
| Reference:
|
[19] W.M. Tulczyjew: The Euler-Lagrange resolution.Lect. Notes in Math. 836, 1980, pp. 22–48. Zbl 0456.58012, MR 0607685 |
| Reference:
|
[20] A. Weil: Théorie des points proches sur les variétés différentiables.Colloque de Géometrie Différentielle, C.N.R.S. (1953), 111–117. Zbl 0053.24903, MR 0061455 |
| . |
