no. 1
Periodic solutions for singular hamiltonian systems and closed geodesics on non-compact riemannian manifolds
Annales de l'I.H.P. Analyse non linéaire, Tome 17 (2000) no. 1, pp. 1-33 
@article{AIHPC_2000__17_1_1_0,
     author = {Tanaka, Kazunaga},
     title = {Periodic solutions for singular hamiltonian systems and closed geodesics on non-compact riemannian manifolds},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {1--33},
     year = {2000},
     publisher = {Gauthier-Villars},
     volume = {17},
     number = {1},
     mrnumber = {1743429},
     zbl = {0955.37040},
     language = {en},
     url = {https://www.numdam.org/item/AIHPC_2000__17_1_1_0/}
}
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Tanaka, Kazunaga. Periodic solutions for singular hamiltonian systems and closed geodesics on non-compact riemannian manifolds. Annales de l'I.H.P. Analyse non linéaire, Tome 17 (2000) no. 1, pp. 1-33. https://www.numdam.org/item/AIHPC_2000__17_1_1_0/

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