Orbites périodiques des systèmes hamiltoniens autonomes
Séminaire Bourbaki : vol. 1979/80, exposés 543-560, Séminaire Bourbaki, no. 22 (1979-1980), Exposé no. 552, p. 156-173
@incollection{SB_1979-1980__22__156_0,
     author = {Desolneux-Moulis, Nicole},
     title = {Orbites p\'eriodiques des syst\`emes hamiltoniens autonomes},
     booktitle = {S\'eminaire Bourbaki : vol. 1979/80, expos\'es 543-560},
     author = {Collectif},
     series = {S\'eminaire Bourbaki},
     publisher = {Springer-Verlag},
     number = {22},
     year = {1979-1980},
     note = {talk:552},
     pages = {156-173},
     zbl = {0479.58008},
     mrnumber = {636522},
     language = {fr},
     url = {http://www.numdam.org/item/SB_1979-1980__22__156_0}
}
Desolneux-Moulis, Nicole. Orbites périodiques des systèmes hamiltoniens autonomes, dans Séminaire Bourbaki : vol. 1979/80, exposés 543-560, Séminaire Bourbaki, no. 22 (1979-1980), Exposé no. 552, pp. 156-173. http://www.numdam.org/item/SB_1979-1980__22__156_0/

[1] R. Abraham, J.E. Marsden - Foundations of Mechanics, 2nd edition, Benjamin. | Zbl 0158.42901

[2] H. Amann, E. Zehnder - Non trivial solutions for a class of non resonance problems and applications to non linear differential equations, à paraître. | Numdam | Zbl 0452.47077

[3] V.I. Arnold - Méthodes mathématiques de la mécanique classique, éditions Mir. | MR 474391 | Zbl 0385.70001

[4] V.I. Arnold, A. Avez - Problèmes ergodiques de la mécanique classique, éditions Gauthier-Villars. | MR 209436 | Zbl 0149.21704

[5] V. Benci, P.H. Rabinowitz - Critical point theorems for indefinite functionals, Inv. Math., Vol 52, fasc. 3(1979), p. 241-274. | MR 537061 | Zbl 0465.49006

[6] M. Berger - On a family of periodic solutions for Hamiltonian systems, J. Diff. Eq., 10(1971), p. 324-335. | MR 280802 | Zbl 0237.34067

[7] G.D. Birkhoff - On the periodic motions of dynamical systems, Acta Math., 50(1927), p. 359-379. | JFM 53.0733.03 | MR 1555257

[8] D. Clark - On periodic solutions of autonomous Hamiltonian systems of ordinary differential equations, Proc. A.M.S., 39(1973), p. 579-584. | MR 315217 | Zbl 0243.34067

[9] F.H. Clarke - Periodic solutions to Hamiltonian inclusions, à paraître J. Diff. Eq. | Zbl 0461.34030

[10] F.H. Clarke, I. Ekeland - Hamiltonian trajectories having prescribed minimal period, Preprint, cahier CEREMADE n° 7822. Note C.R.A.S. t. 287(1978), p. 1013-1015. A paraître Comm. on pure and appl. Math.. | MR 562546 | Zbl 0404.34033

[11] I. Ekeland - Periodic solutions of Hamiltonian equations and a theorem of P. Rabinowitz, J. Diff. Eq., Vol. 34, n° 3 déc. 1979, p. 523-534. | MR 555325 | Zbl 0446.70019

[12] I. Ekeland, J.M. Lasry - Nombre de solutions périodiques des équations de Hamilton, Preprint cahier CEREMADE n° 7902, à paraître Annals of Math. | MR 525925

[13] E.R. Fadell, P.H. Rabonowitz - Generalized cohomological index theories for Lie group actions with an application to bifurcation questions for Hamiltonian systems, Inv. Math., Vol. 45, fasc. 2(1978), p. 139-174. | MR 478189 | Zbl 0403.57001

[14] A.I. Fet, L.A. Lusternik - Variational problems on closed manifolds, Dokl. Akad. Nauk S.S.S.R., 81(1951), p. 17-18. | MR 44760 | Zbl 0045.20903

[15] W.B. Gordon - A theorem on the existence of periodic solutions to Hamiltonian systems with convex potential, J. Diff. Eq., 10(1971), p. 324-335. | MR 292113 | Zbl 0231.35006

[16] Y. Hagihara - Celestial Mechanics, Jap. Soc. for promotion of science, Tokyo 1975. | MR 478841

[17] J. Horn - Beitrage zur Theorie der kleinen Schwingungen, Z. Math. Phys., 48(1903), p. 400-434. | JFM 34.0764.01

[18] W. Klingenberg - Closed geodesics, Grundlehren der Mathematischen Wissenschaften, Vol. 230, Springer 1978. | MR 478069 | Zbl 0397.58018

[19] J.L. Lagrange - Mémoire sur la théorie de la variation des éléments des planètes, Mem. classe Sci. Math. Phys. Inst. France, 1808, Oeuvres complètes, tome VI, p. 713-768.

[20] L. Lusternik, L. Schnirelman - Méthodes topologiques dans les problèmes variationnels, Hermann, Paris, 1934. | Zbl 0011.02803

[21] A. Lyapunov - Problème général de la stabilité des mouvements, Ann. Fac. Sci. de Toulouse, 2(1907), p. 203-474. | Numdam

[22] J. Moser - A theorem by A. Weinstein and bifurcation theory, Report of the University Louvain la Neuve, Janv. 1976. | Zbl 0351.58002

[23] J. Moser - Periodic orbits near an equilibrium and a theorem by Alan Weinstein, Commun. on pure and appl. Math., Vol XXIX, 1976, p. 727-747. | MR 426052 | Zbl 0346.34024

[24] J. Moser - Proof of a generalized form of a fixed point theorem, Geometry and Topology, Rio de Janeiro, July 1976. Lecture Notes n° 597, Springer, p. 464-494. | MR 494305 | Zbl 0358.58009

[25] R.S. Palais - Critical point theory and the minimax principle, Global Analysis, Proc. A.M.S., Vol. XV, p. 185-212. | MR 264712 | Zbl 0212.28902

[26] H. Poincaré - Les méthodes nouvelles de la mécanique céleste, Gauthier-Villars, 1892. | JFM 25.1847.03

[27] P.H. Rabinowitz - Periodic solutions of Hamiltonian systems, Comm. pure and appl. Math., Vol. XXXI, 1978, p. 157-184. | MR 467823 | Zbl 0358.70014

[28] J.T. Schwartz - Non linear functional analysis, Gordon and Breach 1969. | Zbl 0203.14501

[29] C.L. Siegel, J.K. Moser - Lectures on celestial mechanics, Grundlehren des Math. Wiss., n° 187, Springer 1971. | MR 502448 | Zbl 0312.70017

[30] H. Seifert - Periodische Bewegungen mechanischer system, Math. Zeits. 51(1948), p. 197-216. | MR 25693 | Zbl 0030.22103

[31] J. Vey - Orbites périodiques d'un système hamiltonien au voisinage d'un point d'équilibre, Ann. Sci. Nor. Sup., Pisa ser. 4 Vol. 5(1978), p. 757-787. | Numdam | MR 519892 | Zbl 0391.70018

[32] A. Weinstein - Lagrangian submanifolds and hamiltonian systems, Ann. of Math., 98(1973), p. 377-410. | MR 331428 | Zbl 0271.58008

[33] A. Weinstein - Normal modes for non linear hamiltonian systems, Inv. Math., 20(1973), p. 47-57. | MR 328222 | Zbl 0264.70020

[34] A. Weinstein - Periodic orbits for convex hamiltonian systems, Ann. of Math., 108(1978), p. 507-518. | MR 512430 | Zbl 0403.58001

[35] A. Weinstein - Bifurcations and Hamilton's principle, Math. Zeits., 159(1978), p. 235-248. | MR 501163 | Zbl 0366.58003

[36] A. Weinstein - On the hypotheses of Rabinowitz' periodic orbit theorems, J. Diff. Eq., Vol. 33, n° 3(1979), p. 353-358. | MR 543704 | Zbl 0388.58020