@article{AIHPA_1996__65_2_223_0, author = {Crampin, M. and Mart\'\i nez, E. and Sarlet, W.}, title = {Linear connections for systems of second-order ordinary differential equations}, journal = {Annales de l'I.H.P. Physique th\'eorique}, volume = {65}, year = {1996}, pages = {223-249}, mrnumber = {1411267}, zbl = {0912.58002}, language = {en}, url = {http://dml.mathdoc.fr/item/AIHPA_1996__65_2_223_0} }
Crampin, M.; Martínez, E.; Sarlet, W. Linear connections for systems of second-order ordinary differential equations. Annales de l'I.H.P. Physique théorique, Tome 65 (1996) pp. 223-249. http://gdmltest.u-ga.fr/item/AIHPA_1996__65_2_223_0/
[1] The Inverse Problem of the Calculus of Variations for Ordinary Differential Equations, Memoirs of the American Mathematical Society, Vol. 98, 1992. | MR 1115829 | Zbl 0760.49021
and ,[2] Geometrical Methods in the Theory of Ordinary Differential Equations, Springer Verlag, 1983. | MR 695786 | Zbl 0507.34003
,[3] On curvature in Finsler geometry, Trans. Amer. Math. Soc., Vol. 79, 1954, pp. 378-388. | MR 71833 | Zbl 0066.16202
,[4] On a notable connection in Finsler geometry, Houston J. Math., Vol. 19, 1993, pp. 135-180. | MR 1218087 | Zbl 0787.53018
and ,[5] Finsler Geometry and Applications, Ellis Horwood, 1990. | MR 1071171 | Zbl 0702.53001
,[6] A complete set of Bianchi identities for tensor fields along the tangent bundle projection, J. Phys. A: Math. Gen., Vol. 27, 1994, pp. 6617-6632. | MR 1306452 | Zbl 0851.53008
,[7] Complete separability of time-dependent second-order equations, Acta Appl. Math. | Zbl 0842.34009
, , and ,[8] Generalized Bianchi identities for horizontal distributions, Math. Proc. Camb. Phil. Soc., Vol. 94, 1983, pp. 125-132. | MR 704806 | Zbl 0521.53023
,[9] A geometrical version of the Helmholtz conditions in time-dependent Lagrangian dynamics, Phys. A: Math. Gen., Vol. 17, 1984, pp. 1437-1447. | MR 748776 | Zbl 0545.58020
, and ,[10] Towards a geometrical understanding of Douglas's solution of the inverse problem of the calculus of variations, Inverse Problems, Vol. 10, 1994, pp. 245-260. | MR 1269007 | Zbl 0826.58015
, , , and ,[11] Solution of the inverse problem of the calculus of variations, Trans. Amer. Math. Soc., Vol. 50, 1941, pp. 71-128. | JFM 67.1038.01 | MR 4740 | Zbl 0025.18102
,[12] Géometrie des équations différentielles du second ordre, Ann. Inst. H. Poincaré, Phys. Théor., Vol. 45, 1986, pp. 1-28. | Numdam | MR 856446 | Zbl 0624.58011
,[13] Réductibilité de systèmes dynamiques variationnels, Ann. Inst. H. Poincaré, Phys. Théor., Vol. 45, 1986, pp. 359-388. | Numdam | MR 880743 | Zbl 0614.70017
,[14] Estimation de l'entropie des systèmes Lagrangiens sans points conjugués, Ann. Inst. H. Poincaré, Phys. Théor., Vol. 55, 1991, pp. 117-146. | Numdam | MR 1184886 | Zbl 0806.58029
,[15] Structure presque tangente et connections II, Ann. Inst. Fourier (Grenoble), Vol. 22, 1972, pp. 291-338. | Numdam | MR 341361 | Zbl 0236.53027
,[16] Linearization of second order ordinary differential equations via Cartan's equivalence method, J. Diff. Equations, Vol. 77, 1989, pp. 1-15. | MR 980540 | Zbl 0671.34012
, and ,[17] Foundations of Differential Geometry, Interscience, 1963. | MR 152974 | Zbl 0119.37502
and ,[18] Geometría de Ecuaciones Diferenciales Aplicada a la Mecánica, Thesis, University of Zaragoza, Spain; Publicaciones del Seminario García Galdeano, Vol. 36, 1991.
,[19] Geometric characterization of linearizable second-order differential equations, Math. Proc. Camb. Phil. Soc, in press. | Zbl 0851.53009
and ,[20] Derivations of differential forms along the tangent bundle projection, Diff. Geom. Appl., Vol. 2, 1992, pp. 17-43. | MR 1244454 | Zbl 0748.58002
, and ,[21] Derivations of differential forms along the tangent bundle projection II, Diff. Geom. Appl., Vol. 3, 1993, pp. 1-29. | MR 1245556 | Zbl 0770.53018
, and ,[22] Geometric characterization of separable second-order equations, Math. Proc. Camb. Phil. Soc., Vol. 113, 1993, pp. 205-224. | MR 1188830 | Zbl 0803.34010
, and ,[23] Jet bundle geometry, dynamical connections, and the inverse problem of Lagrangian mechanics, Ann. Inst. H. Poincaré, Phys. Théor., Vol. 61, 1994, pp. 17-62. | Numdam | MR 1303184 | Zbl 0813.70004
and ,[24] The inverse problem in the calculus of variations and the geometry of the tangent bundle, Phys. Rep., Vol. 188, 1990, pp. 147-284. | MR 1050526
, , , and ,[25] Derivations of forms along a map: the framework for time-dependent second-order equations, Diff. Geom. Appl., Vol. 5, 1995, pp. 171-203. | MR 1334841 | Zbl 0831.58003
, , and ,[26] The Geometry of Jet Bundles, London Mathematical Society Lecture Note Series, Vol. 142, Cambridge University Press, 1989. | MR 989588 | Zbl 0665.58002
,[27] On differential equations and Cartan's projective connections, Geometry in Partial Differential Equations, ed A. Pràstaro and T. M. Rassias, World Scientific, 1994, pp. 329-344. | Zbl 0957.34009
,[28] Sprays and homogeneous connections on R × TM, Archiv. Math. (Brno), Vol. 28, 1992, pp. 163-173. | MR 1222283 | Zbl 0790.53028
,