Solutions périodiques de systèmes hamiltoniens
Séminaire Bourbaki : volume 1982/83, exposés 597-614, Astérisque, no. 105-106 (1983), Talk no. 603, 24 p.
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     author = {Berestycki, Henri},
     title = {Solutions p\'eriodiques de syst\`emes hamiltoniens},
     booktitle = {S\'eminaire Bourbaki : volume 1982/83, expos\'es 597-614},
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Berestycki, Henri. Solutions périodiques de systèmes hamiltoniens, in Séminaire Bourbaki : volume 1982/83, exposés 597-614, Astérisque, no. 105-106 (1983), Talk no. 603, 24 p. http://www.numdam.org/item/SB_1982-1983__25__105_0/

[1] R. Abraham, J. E. Marsden - Foundations of Mechanics, 2nd edition, Benjamin, New York (1967). | Zbl

[2] H. Amann, E. Zehnder - Nontrivial solutions for a class of nonresonance problems and applications to nonlinear differential equations, Annali Scuola Norm. Sup. Pisa Serie IV, 7(1980), 539-603. | Numdam | MR | Zbl

[3] H. Amann, E. Zehnder - Periodic solutions of asymptotically linear hamiltonian systems, Manuscripta Math. 32(1980), 149-189. | MR | Zbl

[4] A. Ambrosetti, G. Mancini - On a theorem by Ekeland and Lasry concerning the number of periodic hamiltonian trajectories, J. Diff. Equ. 43(1981), 1-6. | Zbl

[5] A. Ambrosetti, G. Mancini - Solutions of minimal period for a class of convex hamiltonian systems, Preprint. | MR

[6] A. Ambrosetti, P. H. Rabinowitz - Dual variational methods in critical point theory and applications, J. Funct. Anal. 14(1973), 349-381. | MR | Zbl

[7] V. I. Arnold - Méthodes mathématiques de la mécanique classique, Editions Mir, Moscou (1976). | MR | Zbl

[8] V. I. Arnold, A. Avez - Problèmes ergodiques de la mécanique classique, Gauthier-Villars, Paris (1967). | MR | Zbl

[9] J.-P. Aubin - Variational principles for differential equations of elliptic, parabolic and hyperbolic type, Cahiers CEREMADE n° 7912, Univ. Paris-Dauphine. | Zbl

[10] J.-P. Aubin, I. Ekeland - Second order evolution equations associated with convex hamiltonians, Bull. Canad. Math. (1979). | MR | Zbl

[11] J. F. G. Auchmuty, R. Beals - Variational solutions of some nonlinear free boundary problems, Arch. Ration. Mech. Anal. 43(1971), 255-271. | MR | Zbl

[12] A. Bahri - Groupes d'homotopie des ensembles de niveaux pour certaines fonctionnelles à gradient Fredholm, à paraître.

[13] A. Bahri, H. Berestycki - Forced vibrations of superquadratic hamiltonian systems, Acta Math. (1983), sous presse. | MR | Zbl

[14] A. Bahri, H. Berestycki - Existence of forced oscillations for some nonlinear differential equations, Comm. Pure Applied Math. (1983), sous presse. | MR | Zbl

[15] V. Benci - Some critical point theorems and applications, Comm. Pure Applied Math. 33(1980), 147-172. | MR | Zbl

[16] V. Benci - On critical point theory for indefinite functionals in the presence of symmetries, Trans. Amer. Math. Soc. 274(1982), 533-572. | MR | Zbl

[17] V. Benci - A geometrical index for the group S1 and some applications to the research of periodic solutions of O.D.E. 's, Comm. Pure Appl. Math. 34(1981), 393-432. | MR | Zbl

[18] V. Benci, P. H. Rabinowitz - Critical point theorems for indefinite functionals, Invent. Math. 52(1979), 241-273. | MR | Zbl

[19] H. Berestycki - Orbites périodiques de systèmes conservatifs, Sém. Goulaouic-Meyer-Schwartz, Exposé n° XXIV, 1981-82, Ec. Polytechnique, Palaiseau. | Numdam | MR | Zbl

[20] H. Berestycki, H. Brezis - On a free boundary problem arising in plasma physics, Nonlinear Analysis, T.M.A. 4(1980), 415-436. | MR | Zbl

[21] H. Berestycki, J. M. Lasry - A topological method for the existence of periodic orbits to conservative systems, Preprint.

[22] H. Berestycki, J. M. Lasry, G. Mancini, B. Ruf - Existence of multiple periodic orbits on star-shaped hamiltonian surfaces, Preprint. | MR

[23] M. S. Berger - Nonlinearity and functional analysis, Academic Press, New York (1987). | MR | Zbl

[24] M. S. Berger - On a family of periodic solutions for hamiltonian systems, J. Diff. Equ. 10(1971), 324-335. | MR | Zbl

[25] H. Brezis - Periodic solutions of nonlinear vibrating strings and duality principle, Bull. A.M.S., à paraître. | Zbl

[26] H. Brezis, J. M. Coron - Periodic solutions of nonlinear wave equations and hamiltonian systems, Amer. J. of Math. 103(1980), 559-570. | MR | Zbl

[27] H. Brezis, J. M. Coron, L. Nirenberg - Free vibrations for a nonlinear wave equation and a theorem of P. Rabinowitz, Comm. Pure Appl. Math. 33(1980), 667-684. | MR | Zbl

[28] H. Brezis, I. Ekeland - Un principe variationnel associé à certaines équations paraboliques, C.R.A.S. 282(1976), 971-974 et 1197-1198. | Zbl

[29] K. C. Chang - Solutions of asymptotically linear operator equations via Morse theory, Comm. Pure Appl. Math. 34(1981), 639-712. | MR | Zbl

[30] F. Clarke - A classical variational principle for periodic hamiltonian trajectories, Proc. Amer. Math. Soc. 76(1979), 186-188. | MR | Zbl

[31] F. Clarke - Periodic solutions to hamiltonian inclusions, J. Diff. Equ. 40(1981), 1-6. | MR | Zbl

[32] F. Clarke, I. Ekeland - Hamiltonian trajectories having prescribed minimal period, Comm. Pure Appl. Math. 33(1980), 103-116. | MR | Zbl

[33] C. Conley - Isolated invariant sets and the Morse index, CBMS Reg. Conf. ser. in Math. n° 38, Amer. Math. Soc. Providence R.I. (1978). | MR | Zbl

[34] C. Conley, E. Zehnder - Morse type index theory for flows and periodic solutions for hamiltonian equations, à paraître. | Zbl

[35] C. Conley, E. Zehnder - The Birkhoff-Lewis fixed point theorem and a conjecture of V.I. Arnold, Version préliminaire.

[36] N. Desolneux-Moulis - Orbites périodiques des systèmes hamiltoniens autonomes, Sém. Bourbaki février 1980, exposé n° 552, Lect. Notes in Math. n° 842, Springer-Verlag (1981). | Numdam | MR | Zbl

[37] I. Ekeland - Periodic solutions of hamiltonian equations and a theorem of P. Rabinowitz, J. Diff. Equ. 34(1979), 523-534. | MR | Zbl

[38] I. Ekeland - Oscillations de systèmes hamiltoniens non linéaires III, Bull. Soc. Math. France 109(1981), 297-330. | Numdam | MR | Zbl

[38B] I. Ekeland - Forced oscillations of nonlinear hamiltonian systems II, Advances Math. 7A(1981), 345-360. | MR | Zbl

[39] I. Ekeland - A perturbation theory near convex hamiltonian systems, Cahiers CEREMADE n° 8226, Univ. Paris-Dauphine, à paraître. | Zbl

[40] I. Ekeland - La théorie des perturbations au voisinage des systèmes hamiltoniens convexes, Sém. Goulaouic-Meyer-Schwartz décembre 1981, Exposé n° 7, Ec. Polytechnique, Palaiseau. | Numdam | Zbl

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

[42] I. Ekeland, J. M. Lasry - Problèmes variationnels non convexes en dualité, C.R.A.S. Paris, Série A 291(1980), 493-496. | MR | Zbl

[43] I. Ekeland, R. Temam - Convex analysis and variational problems, North Holland, New York (1976). | MR | Zbl

[44] R. E. Fadell, P. H. Rabinowitz - Generalized cohomological index theories for Lie group actions with an application to bifurcation questions for hamiltonian systems, Invent. Math. 45(1978), 139-174. | MR | Zbl

[45] E. R. Fadell, S. Husseini, P. H. Rabinowitz - Borsuk-Ulam theorem for arbitrary S1-actions and applications, MRC Report 2301, Madison Wis. USA.

[45B] M. Girardi, M. Matzeu - Some results on solutions of minimal period to superquadratic hamiltonian systems, Preprint. | MR

[46] W. B. Gordon - A theorem on the existence of periodic solutions to hamiltonian systems with convex potentials, J. Diff. Equ. 10(1971), 324-335. | MR | Zbl

[47] H. Hofer - A simple proof for a result of I. Ekeland and J.M. Lasry concerning the number of periodic hamiltonian trajectories on a prescribed energy surface, Preprint.

[47B] S. Y. Husseini - The equivariant J-homomorphism for arbitrary S1-action, Preprint.

[48] L. Liusternik, L. Schnirelman - Méthodes topologiques dans les problèmes variationnals, Hermann, Paris (1934). | Zbl

[49] A. Liapunov - Problème général de la stabilité des mouvements, Ann. Fac. Sci. Toulouse 2(1907), 203-474.

[50] J. L. Lions, E. Magenes - Problèmes aux limites non homogènes et applications, Dunod, Paris (1968). | Zbl

[51] A. Marino, G. Prodi - Metodi perturbativi nella teoria di Morse, Boll. U.M.I. 11(1975), 1-32. | MR | Zbl

[52] J. Mawin - Contractive mappings and periodically perturbed conservative systems, Arch. Math. 12(1976), 67-74. | MR | Zbl

[53] J. Moser - Periodic orbits near an equilibrium and a theorem by A. Weinstein, Comm. Pure Appl. Math. 29(1976), 727-747. | MR | Zbl

[54] W. M. Ni - Some minimax principles and their applications in nonlinear elliptic equations, J. Analyses Math. 37(1980), 248-275. | MR | Zbl

[55] L. Nirenberg - Comments on nonlinear problems, Proceed. Conf. Catania (Italie), septembre 1981. | MR

[56] L. Nirenberg - Variational and topological methods in nonlinear problems, Bull. Amer. Math. Soc. 4(1981), 267-302. | MR | Zbl

[57] H. Poincare - Les méthodes nouvelles de la mécanique céleste, Gauthier-Villars, Paris (1982). | JFM

[58] R. Palais - Critical point theory and the minimax principle, Proc. Symp. Pure Math. vol. 15, Amer. Math. Soc. Providence R.I. (1970), 185-212. | MR | Zbl

[59] P. H. Rabinowitz - Variational methods for nonlinear eigenvalue problems, (CIME, Varenna 1974), Ediz. Cremonese, Rome (1974). | MR

[60] P. H. Rabinowitz - Free vibrations for a semi-linear wave equation, Comm. Pure Appl. Math. 31(1978), 31-68. | MR | Zbl

[61] P. H. Rabinowitz - Periodic solutions of hamiltonian systems, Comm. Pure Appl. Math. 31(1978), 157-184. | MR | Zbl

[62] P. H. Rabinowitz - A variational method for finding periodic solutions of differential equations, Nonlinear evolution equations (M.G. Crandall Ed.) Academic Press, New York (1978), 225-251. | MR | Zbl

[63] P. H. Rabinowitz - Periodic solutions of hamiltonian systems : A survey, MRC Techn. Report n° 2154, Univ. Wisconsin-Madison (1980).

[64] P. H. Rabinowitz - Subharmonic solutions of hamiltonian systems, Comm. Pure Math. 33(1980), 609-633. | MR | Zbl

[65] P. H. Rabinowitz - Periodic solutions of large norm of hamiltonian systems, Preprint. | MR

[66] P. H. Rabinowitz - Multiple critical points of perturbed symmetric functionals, Trans. Amer. Math. Soc. 272(1982), 753-769. | MR | Zbl

[67] H. Seifert - Periodischer bewegungen mechanischer systeme, Math. Zeit. 51(1948), 197-216. | MR | Zbl

[68] C. L. Siegel, J. Moser - Lectures on celestial mechanics, Springer-Verlag, New York (1971) ; Grundlehren Math. vol. 187. | MR | Zbl

[69] M. Schatzman - A class of nonlinear differential equations of second order in time, Nonlinear Analysis, T.M.A. 2(1978), 355-373. | MR | Zbl

[70] A. Weinstein - Lagragian submanifolds and hamiltonian systems, Ann. Math. 98 (1973), 377-410. | MR | Zbl

[71] A. Weinstein - Normal modes for nonlinear hamiltonian systems, Invent. Math. 20 (1973), 47-57. | MR | Zbl

[72] A. Weinstein - Periodic orbits for convex hamiltonian systems, Ann. Math. 108 (1987), 507-518. | MR | Zbl

[73] A. Weinstein - Bifurcations and Hamilton's principle, Math. Zeit. 159(1978), 235-248. | MR | Zbl

[74] A. Weinstein - On the hypotheses of Rabinowitz' periodic orbit theorems, J. Diff. Equ. 33(1979), 353-358. | MR | Zbl

[75] M. Willem - Subharmonic oscillations of convex hamiltonian systems, Preprint. | MR

[76] M. Willem - Subharmonic oscillations of nonlinear systems, Proceed. Conf. "Equa. diff. 82", Würzburg, à paraître. | Zbl