no. 2
Linear connections for systems of second-order ordinary differential equations
Annales de l'I.H.P. Physique théorique, Tome 65 (1996) no. 2, pp. 223-249. 
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     title = {Linear connections for systems of second-order ordinary differential equations},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     pages = {223--249},
     publisher = {Gauthier-Villars},
     volume = {65},
     number = {2},
     year = {1996},
     mrnumber = {1411267},
     zbl = {0912.58002},
     language = {en},
     url = {http://archive.numdam.org/item/AIHPA_1996__65_2_223_0/}
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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) no. 2, pp. 223-249. http://archive.numdam.org/item/AIHPA_1996__65_2_223_0/

[1] I. Anderson and G. Thompson, The Inverse Problem of the Calculus of Variations for Ordinary Differential Equations, Memoirs of the American Mathematical Society, Vol. 98, 1992. | MR | Zbl

[2] V.I. Arnold, Geometrical Methods in the Theory of Ordinary Differential Equations, Springer Verlag, 1983. | MR | Zbl

[3] L. Auslander, On curvature in Finsler geometry, Trans. Amer. Math. Soc., Vol. 79, 1954, pp. 378-388. | MR | Zbl

[4] D. Bao and S.S. Chern, On a notable connection in Finsler geometry, Houston J. Math., Vol. 19, 1993, pp. 135-180. | MR | Zbl

[5] A. Bejancu, Finsler Geometry and Applications, Ellis Horwood, 1990. | MR | Zbl

[6] G. Byrnes, 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 | Zbl

[7] F. Cantrijn, W. Sarlet, A. Vandecasteele and E. Martínez, Complete separability of time-dependent second-order equations, Acta Appl. Math. | Zbl

[8] M. Crampin, Generalized Bianchi identities for horizontal distributions, Math. Proc. Camb. Phil. Soc., Vol. 94, 1983, pp. 125-132. | MR | Zbl

[9] M. Crampin, G.E. Prince and G. Thompson, A geometrical version of the Helmholtz conditions in time-dependent Lagrangian dynamics, Phys. A: Math. Gen., Vol. 17, 1984, pp. 1437-1447. | MR | Zbl

[10] M. Crampin, W. Sarlet, E. Martínez, G. Byrnes and G.E. Prince, 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 | Zbl

[11] J. Douglas, Solution of the inverse problem of the calculus of variations, Trans. Amer. Math. Soc., Vol. 50, 1941, pp. 71-128. | JFM | MR | Zbl

[12] P. Foulon, Géometrie des équations différentielles du second ordre, Ann. Inst. H. Poincaré, Phys. Théor., Vol. 45, 1986, pp. 1-28. | Numdam | MR | Zbl

[13] P. Foulon, Réductibilité de systèmes dynamiques variationnels, Ann. Inst. H. Poincaré, Phys. Théor., Vol. 45, 1986, pp. 359-388. | Numdam | MR | Zbl

[14] P. Foulon, Estimation de l'entropie des systèmes Lagrangiens sans points conjugués, Ann. Inst. H. Poincaré, Phys. Théor., Vol. 55, 1991, pp. 117-146. | Numdam | MR | Zbl

[15] J. Grifone, Structure presque tangente et connections II, Ann. Inst. Fourier (Grenoble), Vol. 22, 1972, pp. 291-338. | Numdam | MR | Zbl

[16] C. Grissom, G. Thompson and G. Wilkens, Linearization of second order ordinary differential equations via Cartan's equivalence method, J. Diff. Equations, Vol. 77, 1989, pp. 1-15. | MR | Zbl

[17] S. Kobayashi and K. Nomizu, Foundations of Differential Geometry, Interscience, 1963. | MR | Zbl

[18] E. Martínez, Geometría de Ecuaciones Diferenciales Aplicada a la Mecánica, Thesis, University of Zaragoza, Spain; Publicaciones del Seminario García Galdeano, Vol. 36, 1991.

[19] E. Martínez and J.F. Cariñena, Geometric characterization of linearizable second-order differential equations, Math. Proc. Camb. Phil. Soc, in press. | Zbl

[20] E. Martínez, J.F. Cariñena and W. Sarlet, Derivations of differential forms along the tangent bundle projection, Diff. Geom. Appl., Vol. 2, 1992, pp. 17-43. | MR | Zbl

[21] E. Martínez, J.F. Cariñena and W. Sarlet, Derivations of differential forms along the tangent bundle projection II, Diff. Geom. Appl., Vol. 3, 1993, pp. 1-29. | MR | Zbl

[22] E. Martínez, J.F. Cariñena and W. Sarlet, Geometric characterization of separable second-order equations, Math. Proc. Camb. Phil. Soc., Vol. 113, 1993, pp. 205-224. | MR | Zbl

[23] E. Massa and E. Pagani, 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 | Zbl

[24] G. Morandi, C. Ferrario, G., Lo Vecchio, G. Marmo and C. Rubano, The inverse problem in the calculus of variations and the geometry of the tangent bundle, Phys. Rep., Vol. 188, 1990, pp. 147-284. | MR

[25] W. Sarlet, A. Vandecasteele, F. Cantrijn and E. Martínez, Derivations of forms along a map: the framework for time-dependent second-order equations, Diff. Geom. Appl., Vol. 5, 1995, pp. 171-203. | MR | Zbl

[26] D.J. Saunders, The Geometry of Jet Bundles, London Mathematical Society Lecture Note Series, Vol. 142, Cambridge University Press, 1989. | MR | Zbl

[27] Y.R. Romanovsky, 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

[28] A. Vondra, Sprays and homogeneous connections on R × TM, Archiv. Math. (Brno), Vol. 28, 1992, pp. 163-173. | MR | Zbl