Orbites périodiques dans le problème des trois corps
Séminaire Bourbaki : volume 1992/93, exposés 760-774, Astérisque, no. 216 (1993), Exposé no. 774, 17 p.
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     author = {Viterbo, Claude},
     title = {Orbites p\'eriodiques dans le probl\`eme des trois corps},
     booktitle = {S\'eminaire Bourbaki : volume 1992/93, expos\'es 760-774},
     series = {Ast\'erisque},
     note = {talk:774},
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     publisher = {Soci\'et\'e math\'ematique de France},
     number = {216},
     year = {1993},
     mrnumber = {1246404},
     zbl = {0801.70007},
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Viterbo, Claude. Orbites périodiques dans le problème des trois corps, dans Séminaire Bourbaki : volume 1992/93, exposés 760-774, Astérisque, no. 216 (1993), Exposé no. 774, 17 p. http://archive.numdam.org/item/SB_1992-1993__35__377_0/

[A-CZ 1] Ambrosetti, A. and Coti-Zelati, V., Critical points with lack of compactness and applications to singular dynamical systems,, Annali Mat. Pura Appl. 149 (1987), 237-259. | MR | Zbl

[A-CZ 2] Ambrosetti, A. and Coti-Zelati, V., Periodic solutions of singular dynamical systems, in "Periodic solutions of Hamiltonian systems and related topics," P.H Rabinowitz et al eds, Nato ASI Series, Reidel, 1987, pp. 1-10. | MR | Zbl

[A-CZ 3] Ambrosetti, A. and Coti-Zelati, V., Noncollision orbits for a class of Keplerian like potentials, Ann. Inst. Henri Poincaré, Analyse Non Linéaire 5 (1988), 287-295. | Numdam | MR | Zbl

[A-CZ 4] Ambrosetti, A. and Coti-Zelati, V., Perturbation of hamiltonian systems with Kepterian potentials, Math. Zeitschrift 201 (1989), 227-242. | MR | Zbl

[A-CZ 5] Ambrosetti, A. and Coti-Zelati, V., Closed orbits of fixed energy for a class of n-body problems, Ann. Inst. Henri Poincaré, Analyse Non Linéaire 9 (1992), 187-200. | Numdam | MR | Zbl

[A-CZ 6] Ambrosetti, A. and Coti-Zelati, V., "Periodic solutions of singular Lagrangian systems," Birkhaüser, 1993. | MR | Zbl

[B ] Bahri, A.,, Variational contribution of periodic orbits obtained by the Birkhoff-- Lewis method, preprint, Department of Mathematics, Rutgers University, New Brunswick, N.J. 08903, U.S.A..

[B-C 1] Bahri, A., Coron, J-M., Une théorie des points critiques à l'infini pour l'équation de Yamabe et le problème de Kazdan-Warner, C. R. Acad. Sci. Paris Ser. I Math. 300 (1985), 513-516. | MR | Zbl

[B-C 2] Bahri, A., Coron, J-M., On a nonlinear elliptic equation involving the critical Sobolev exponent: the effect of the topology of the domain, Comm. Pure and Appl. Math. 41 (1988), 253-294. | MR | Zbl

[B-C 3] Bahri, A., Coron, J-M., The scalar-curvature problem on the standard three-dimensional sphere.-, J. Funct. Anal. 95 (1991), 106-172. | MR | Zbl

[B-L 1] Bahri, A., Lions, P. L., Remarques sur la théorie variationelle des points critiques et applications, C.R. Acad.Sci.,Paris 301 (1985), p. 145-147. | MR | Zbl

[B-L 2] Bahri, A. and Lions, P. L., Morse index of some min-max critical points I. Applications to multiplicity results, Comm. Pure Appl. Math. 41 (1988), 1027-1037. | MR | Zbl

[B-D'O] Bahri, A. et D'Onofrio, B., Exponential growth of the number of periodic orbits for three body type problems, Maghreb Math. Rev. 1 (1992), 1-14. | MR | Zbl

[B-R 1] Bahri, A. et Rabinowitz, P., A minmax method for a class of Hamiltonian systems with singular potentials, J. Functional Anal. 8 (1989), 561-649. | Zbl

[B-R 2] Bahri, A. et Rabinowitz, P., Periodic solutions of Hamiltonian systems of three-body type, Ann. Inst. Poincaré Analyse Non Linéaire 82 (1991), 412-428. | Numdam

[B-CZ] Bessi, U. et Coti-Zelati, V., Symmetries and non-collision closed orbits for planar N-Body type problems, Non Linear Anal. TMA 16 (1991), 587-598. | MR | Zbl

[Bi] Birkhoff, G., "Dynamical systems,", Amer. Math. Soc., Providence,R.I., 1924.

[Br] Brézis, H., Points critiques dans les problèmes variationnels sans compacité, Séminaire Bourbaki, Exposé 698, Astérisque 161-162 (1988), 239-256. | Numdam | MR | Zbl

[Co] Conley, C. C., "Isolated Invariant Sets and their Morse Index," C.B.M.S. Reg. Conf. Series in Math. n° 38, Amer. Math. Soc., Providence,R.I., 1978. | MR | Zbl

[CZ 1] Coti-Zelati, V., Periodic solutions for N-body type problems, Ann. Inst. Henri Poincaré, Analyse Non Linéaire 7 (1990), 477-492. | Numdam | MR | Zbl

[CZ 2] Coti-Zelati, V., A class of periodic solutions of the N-body problem, Cel. Mech. and Dyn. Astr. 46 (1989), 177-186. | MR | Zbl

[DA] Dell'Antonio, G., Finding non-collision periodic solutions to a perturbed N-body Kepler problem, preprint Dip. di Matematica Univ. Roma "La Sapienza".

[F] Floer, A., Witten's complex and infinite-dimensional Morse theory, J. of Differential Geom. 30 (1989), 207-221.. | MR | Zbl

[G] Gordon, W., Conservative dynamical systems involving strong forces, Trans. Amer. Math. Soc. 204 (1975), 113-135. | MR | Zbl

[Gr] Greco, C., Periodic solutions of a class of singular Hamiltonian systems, Nonlinear Analysis 12 (1988), 259-269. | MR | Zbl

[K] Klingenberg, W., "Lectures on Closed Geodesics," Grundlehren der Math. Wissenschaften, Band 230, Springer-Verlag, Berlin-Heidelberg-NewYork, 1978. | MR | Zbl

[L] Lions, P. L., The concentration compactness principle in the calculus of Variations (Part 1 and 2), Revista Matematica Iberoamericana 1 (1985), 45 and 145. | MR

[M-T 1] Majer, P. et Teracini, S., Periodic solutions to some n-body type problems, Arch. Rat. Mech. Anal. (to appear).

[M-T 2] Majer, P. et Teracini, S., Periodic solutions to some n-body type problems: the fixed energy case, Duke Math. Jour. (to appear). | Zbl

[M-T 3] Majer, P. et Teracini, S., Multiple periodic solutions to some N-body type problems via a collision index, preprint, Dip. di Matematica del Politecnico di Milano, Pzza L. da Vinci 32, Milano.

[R] Riahi, H., Periodic orbits of n-body type problems, PhD dissertation, Department of Mathematics, Rutgers University, New Brunswik, N.J. 08903, U.S.A..

[S-T] Serra, E. et Teracini, S., Collisionless periodic solutions to some three-body problems, Arch. Rat. Mech. Anal. 120 (1992), 305-325. | MR | Zbl

[Si-M] Siegel, C. L. et Moser, J., "Lectures on celestial mechanics," Springer-Verlag, 1971. | MR | Zbl

[Su] Sundman, Acta Soc. Sci. Fenn. 35 (1909).

[Su-VP] Sullivan, D., Vigué-Poirrier, M., The homology theory of the closed geodesic problems, Jour. of Differential Geometry 11 (1976), 633-644. | MR | Zbl

[Ta 1] Tanaka, K., Morse indices at critical points related to the symmetric mountain pass theorem and applications, Comm. Partial Diff. Eq. 14 (1989), 99-128. | MR | Zbl

[Ta 2] Tanaka, K., Non-collision solutions for a second order singular Hamiltonian system with weak force, preprint.

[V ] Viterbo, C., Indice de Morse des points critiques obtenus par minimax, Annales de l'Institut Henri Poincaré: Analyse non linéaire 5 (1988), 221-225. | Numdam | MR | Zbl