Orbites périodiques dans le problème des trois corps

Claude Viterbo

Séminaire Bourbaki (1992-1993)

  • Volume: 35, page 377-393
  • ISSN: 0303-1179

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Viterbo, Claude. "Orbites périodiques dans le problème des trois corps." Séminaire Bourbaki 35 (1992-1993): 377-393. <http://eudml.org/doc/110176>.

@article{Viterbo1992-1993,
author = {Viterbo, Claude},
journal = {Séminaire Bourbaki},
keywords = {strong-force type potential; existence; critical points at infinity; variational problem; Conley's theory; isolated invariant sets; Morse index},
language = {fre},
pages = {377-393},
publisher = {Société Mathématique de France},
title = {Orbites périodiques dans le problème des trois corps},
url = {http://eudml.org/doc/110176},
volume = {35},
year = {1992-1993},
}

TY - JOUR
AU - Viterbo, Claude
TI - Orbites périodiques dans le problème des trois corps
JO - Séminaire Bourbaki
PY - 1992-1993
PB - Société Mathématique de France
VL - 35
SP - 377
EP - 393
LA - fre
KW - strong-force type potential; existence; critical points at infinity; variational problem; Conley's theory; isolated invariant sets; Morse index
UR - http://eudml.org/doc/110176
ER -

References

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  1. [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. Zbl0642.58017MR932787
  2. [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. Zbl0632.34042MR920605
  3. [A-CZ 3] Ambrosetti, A. and Coti-Zelati, V., Noncollision orbits for a class of Keplerian like potentials, Ann. Inst. Henri Poincaré, Analyse Non Linéaire5 (1988), 287-295. Zbl0667.58055MR954474
  4. [A-CZ 4] Ambrosetti, A. and Coti-Zelati, V., Perturbation of hamiltonian systems with Kepterian potentials, Math. Zeitschrift201 (1989), 227-242. Zbl0653.34032MR997224
  5. [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 Linéaire9 (1992), 187-200. Zbl0757.70007MR1160848
  6. [A-CZ 6] Ambrosetti, A. and Coti-Zelati, V., "Periodic solutions of singular Lagrangian systems," Birkhaüser, 1993. Zbl0785.34032MR1267225
  7. [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.. 
  8. [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. Zbl0585.58005MR792378
  9. [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. Zbl0649.35033MR929280
  10. [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. Zbl0722.53032MR1087949
  11. [B-L 1] Bahri, A., Lions, P.L., Remarques sur la théorie variationelle des points critiques et applications, C.R. Acad.Sci.,Paris301 (1985), p. 145-147. Zbl0589.58007MR801948
  12. [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. Zbl0645.58013MR968487
  13. [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. Zbl0801.70006MR1252384
  14. [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. Zbl0681.70018
  15. [B-R 2] Bahri, A. et Rabinowitz, P., Periodic solutions of Hamiltonian systems of three-body type, Ann. Inst. Poincaré Analyse Non Linéaire82 (1991), 412-428. 
  16. [B-CZ] Bessi, U. et Coti-Zelati, V., Symmetries and non-collision closed orbits for planar N-Body type problems, Non Linear Anal. TMA16 (1991), 587-598. Zbl0715.70016MR1094320
  17. [Bi] Birkhoff, G., "Dynamical systems,", Amer. Math. Soc., Providence,R.I., 1924. 
  18. [Br] Brézis, H., Points critiques dans les problèmes variationnels sans compacité, Séminaire Bourbaki, Exposé 698, Astérisque161-162 (1988), 239-256. Zbl0860.58007MR992212
  19. [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. Zbl0397.34056MR511133
  20. [CZ 1] Coti-Zelati, V., Periodic solutions for N-body type problems, Ann. Inst. Henri Poincaré, Analyse Non Linéaire7 (1990), 477-492. Zbl0723.70010MR1138534
  21. [CZ 2] Coti-Zelati, V., A class of periodic solutions of the N-body problem, Cel. Mech. and Dyn. Astr.46 (1989), 177-186. Zbl0684.70006MR1044425
  22. [DA] Dell'Antonio, G., Finding non-collision periodic solutions to a perturbed N-body Kepler problem, preprint Dip. di Matematica Univ. Roma "La Sapienza". 
  23. [F] Floer, A., Witten's complex and infinite-dimensional Morse theory, J. of Differential Geom.30 (1989), 207-221.. Zbl0678.58012MR1001276
  24. [G] Gordon, W., Conservative dynamical systems involving strong forces, Trans. Amer. Math. Soc.204 (1975), 113-135. Zbl0276.58005MR377983
  25. [Gr] Greco, C., Periodic solutions of a class of singular Hamiltonian systems, Nonlinear Analysis12 (1988), 259-269. Zbl0648.34048MR928560
  26. [K] Klingenberg, W., "Lectures on Closed Geodesics," Grundlehren derMath. Wissenschaften, Band230, Springer-Verlag, Berlin-Heidelberg-NewYork, 1978. Zbl0397.58018MR478069
  27. [L] Lions, P.L., The concentration compactness principle in the calculus of Variations (Part 1 and 2), Revista Matematica Iberoamericana1 (1985), 45 and 145. Zbl0704.49005MR850686
  28. [M-T 1] Majer, P. et Teracini, S., Periodic solutions to some n-body type problems, Arch. Rat. Mech. Anal. (to appear). 
  29. [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). Zbl0807.70009
  30. [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. 
  31. [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.. 
  32. [S-T] Serra, E. et Teracini, S., Collisionless periodic solutions to some three-body problems, Arch. Rat. Mech. Anal.120 (1992), 305-325. Zbl0773.70009MR1185563
  33. [Si-M] Siegel, C.L. et Moser, J., "Lectures on celestial mechanics," Springer-Verlag, 1971. Zbl0817.70001MR502448
  34. [Su] Sundman, Acta Soc. Sci. Fenn.35 (1909). 
  35. [Su-VP] Sullivan, D., Vigué-Poirrier, M., The homology theory of the closed geodesic problems, Jour. of Differential Geometry11 (1976), 633-644. Zbl0361.53058MR455028
  36. [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. Zbl0669.34035MR973271
  37. [Ta 2] Tanaka, K., Non-collision solutions for a second order singular Hamiltonian system with weak force, preprint. Zbl0781.58036
  38. [V ] Viterbo, C., Indice de Morse des points critiques obtenus par minimax, Annales de l'Institut Henri Poincaré: Analyse non linéaire5 (1988), 221—225. Zbl0695.58007MR954472

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