Periodic solutions for a class of Lorenz-lagrangian systems
Annales de l'I.H.P. Analyse non linéaire, Tome 5 (1988) no. 3, pp. 211-220. 
@article{AIHPC_1988__5_3_211_0,
     author = {Toland, J. F.},
     title = {Periodic solutions for a class of {Lorenz-lagrangian} systems},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {211--220},
     publisher = {Gauthier-Villars},
     volume = {5},
     number = {3},
     year = {1988},
     mrnumber = {954471},
     zbl = {0657.34042},
     language = {en},
     url = {http://archive.numdam.org/item/AIHPC_1988__5_3_211_0/}
}
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Toland, J. F. Periodic solutions for a class of Lorenz-lagrangian systems. Annales de l'I.H.P. Analyse non linéaire, Tome 5 (1988) no. 3, pp. 211-220. http://archive.numdam.org/item/AIHPC_1988__5_3_211_0/

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[2] V.V. Kozlov, Calculus of Variations in the Large and Classical Mechanics, Russ. Math. Surveys, Vol. 40, 1985, pp. 37-71. | MR | Zbl

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[4] J.F. Toland, An Index for Hamiltonian Systems with a Natural Order Structure. In Nonlinear Functional Analysis and its Applications, D. Riedel, 1986, pp. 147-161. | MR | Zbl