Closed geodesics for the Jacobi metric and periodic solutions of prescribed energy of natural hamiltonian systems
Annales de l'I.H.P. Analyse non linéaire, Volume 1 (1984) no. 5, p. 401-412
@article{AIHPC_1984__1_5_401_0,
     author = {Benci, Vieri},
     title = {Closed geodesics for the Jacobi metric and periodic solutions of prescribed energy of natural hamiltonian systems},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     publisher = {Gauthier-Villars},
     volume = {1},
     number = {5},
     year = {1984},
     pages = {401-412},
     zbl = {0588.35007},
     mrnumber = {779876},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_1984__1_5_401_0}
}
Benci, V. Closed geodesics for the Jacobi metric and periodic solutions of prescribed energy of natural hamiltonian systems. Annales de l'I.H.P. Analyse non linéaire, Volume 1 (1984) no. 5, pp. 401-412. http://www.numdam.org/item/AIHPC_1984__1_5_401_0/

[AM] A. Ambrosetti, G. Mancini, On a theorem by Ekeland and Lasry concerning the number of periodic Hamiltonian trajectories. J. Diff. Equ., t. 43, 1981, p. 1-6. | Zbl 0492.70018

[A] V.I. Arnold, Méthodes mathématiques de la mécanique classique, Éditions Mir, Moscou, 1976. | MR 474391 | Zbl 0385.70001

[B] V. Benci, Normal modes of a Lagrangian system constrained in a potential well, Ann. Inst. H. Poincaré, t. 1, 1984, p. 379-400. | Numdam | MR 779875 | Zbl 0561.58006

[Br] H. Berestycki, Solutions périodiques des systèmes Hamiltoniens. Séminaire N. Bourbaki, Volume 1982-1983. [BLMR] H. Berestycki, J.M. Lasry, G. Mancini, R. Ruf, Existence of multiple periodic orbits on star-shaped hamiltonian surfaces. Preprint.

[EL] I. Ekeland, J.M. Lasry, On the number of periodic trajectories for a hamiltonian flow on a convex energy surface, Ann. Math., t. 112, 1980, p. 283-319. | MR 592293 | Zbl 0449.70014

[GZ] H. Gluck, W. Ziller, Existence of periodic motions of conservative systems, in Seminar on Minimal Submanifold, E. Bombieri Ed., Princeton University Press, 1983. | MR 795229 | Zbl 0546.58040

[G] H. Goldstain, Classical Mechanics, Addison-Wesley, 1981.

[H] K. Hayashi, Periodic solutions of classical Hamiltonian systems, Tokyo J. Math., t. 6, 1983. | MR 732099 | Zbl 0498.58010

[M] J. Moser, Periodic orbits near an equilibrium and a theorem by A. Weinstein, Comm. Pure Appl. Math., t. 29, 1976, p. 727-747. | Zbl 0346.34024

[R1] P.H. Rabinowitz, Periodontic solutions of Hamiltonian systems' a survey, SIAM J. Math. Anal., t. 13, 1982. | MR 653462 | Zbl 0521.58028

[R2] P.H. Rabinowitz, Periodic solutions of a Hamiltonian system on a prescribed energy surface, J. Differential Equations, t. 33, 1979, p. 336-352. | MR 543703 | Zbl 0424.34043

[S] H. Seifert, Periodischer bewegungen mechanischer Systeme, Math. Zeit., t. 51, 1948, p. 197-216. | MR 25693 | Zbl 0030.22103

[W] A. Weinstein, Normal modes for nonlinear Hamiltonian systems, Invent. Math., t. 20, 1973, p. 47-57. | MR 328222 | Zbl 0264.70020