Francaviglia, Mauro; Krupka, Demeter
The hamiltonian formalism in higher order variational problems
Annales de l'I.H.P. Physique théorique, Tome 37 (1982) no. 3 , p. 295-315
Zbl 0516.70022 | MR 694590
⇒ un erratum à cet article Comment by the editors on the paper : “The hamiltonian formalism in higher order variational problems”
URL stable : http://www.numdam.org/item?id=AIHPA_1982__37_3_295_0

Bibliographie

[1] P. Dedecker, On the Generalization of Symplectic Geometry to Multiple Integrals in the Calculus of Variations, in Differential Geometrical Methods in Mathematical Physics, K. Bleuler ed., Lecture Notes in Math., t. 570, Springer-Verlag, Berlin, 1975, p. 395-496. MR 458478 | Zbl 0352.49018

[2] A. Trautman, Invariance of Lagrangian systems, in General Relativity: Papers in honour of J. L. Synge, L. o'Raifeartaigh ed., Clarendon Press, Oxford, 1972, p. 85-99. MR 503424 | Zbl 0273.58004

[3] H. Goldschmidt, S. Sternberg, Ann. Inst. Fourier (Grenoble), t. 23, 1973, p. 203- 267. Numdam | MR 341531 | Zbl 0243.49011

[4] P.L. Garcia, The Poincaré-Cartan Invariant in the Calculus of Variations, in Symposia Math., t. 14, Academic Press, New York, 1974, p. 219-246. MR 406246 | Zbl 0303.53040

[5] P.L. Garcia, A. Péréz-Rendon, Comm. Math. Phys., t. 13, 1969, p. 24-44. MR 256681 | Zbl 0175.24703

[6] V. Aldaya, J.A. De Azcárrága, Geometric Formulation of Classical Mechanics and Field Theory, Rivista Nuovo Cimento, Ser. 3, t. 3, 10, 1980. MR 604503

[7] D. Krupka, Some Geometric Aspects of Variational Problems in Fibered Manifold, Folia Fac. Sci. Nat. U. J. E. P. Brunensis, t. 15, 10, 1973, p. 1-65.

[8] D. Krupka, J. Math. Anal. Appl., t. 49, 1975, p. 180-206, 469-476. Zbl 0312.58002

[9] D. Krupka, Natural Lagrangian Structures, Banach Center Publications (Differential Geometry Semester, Warsaw, October 1979). Zbl 0572.58007

[10] P.R. Rodrigues, J. Math. Phys., t. 18, 1977, p. 1720-1723. MR 455040 | Zbl 0373.70018

[11] I. Kolář, Scripta Fac. Sci. Nat. U. J. E. P. Brunensis, Physica, n°) 3-4, t. 5, 1975, p. 249-254. MR 442978

[12] R. Ragionieri, R. Ricci, Boll. Un. Mat. Italiana (5), t. 18 B, 1981, p. 119-130. MR 613378 | Zbl 0481.58019

[13] P.R. Rodrigues, Comptes Rendus Ac. Sci. Paris, t. 282 A, 1976, p. 1307-1309. Zbl 0329.53031

[14] L.M.C.S. Rodrigues, P.R. Rodrigues, Am. J. Phys., t. 38 (5), 1970, p. 557-560.

[15] V. Aldaya, J.A. De Azcárrága, J. Math. Phys., t. 19 (9), 1978, p. 1869-1875. MR 496116 | Zbl 0415.58010

[16] R. Hermann, Differential Geometry and the Calculus of Variations. Academic Press, New York, 1968. MR 233313 | Zbl 0219.49023

[17] D. Krupka, Přirozené Lagrangeovy struktury, DrSc. Dissertation, Mathematical Institute of the ČSAV, Prague, 1978. MR 527720

[18] D. Krupka, Lepagean Forms and Higher Order Variational Theories, in : Proceedings IUTAM-ISIMM Symposium, Torino June 1982, A. LICHEROWICZ et al. eds. (to appear in 1983). MR 773488 | Zbl 0572.58003