@incollection{SB_1982-1983__25__105_0, author = {Berestycki, Henri}, title = {Solutions p\'eriodiques de syst\`emes hamiltoniens}, booktitle = {S\'eminaire Bourbaki : volume 1982/83, expos\'es 597-614}, series = {Ast\'erisque}, note = {talk:603}, pages = {105--128}, publisher = {Soci\'et\'e math\'ematique de France}, number = {105-106}, year = {1983}, mrnumber = {728984}, zbl = {0526.58016}, language = {fr}, url = {http://archive.numdam.org/item/SB_1982-1983__25__105_0/} }
TY - CHAP AU - Berestycki, Henri TI - Solutions périodiques de systèmes hamiltoniens BT - Séminaire Bourbaki : volume 1982/83, exposés 597-614 AU - Collectif T3 - Astérisque N1 - talk:603 PY - 1983 SP - 105 EP - 128 IS - 105-106 PB - Société mathématique de France UR - http://archive.numdam.org/item/SB_1982-1983__25__105_0/ LA - fr ID - SB_1982-1983__25__105_0 ER -
%0 Book Section %A Berestycki, Henri %T Solutions périodiques de systèmes hamiltoniens %B Séminaire Bourbaki : volume 1982/83, exposés 597-614 %A Collectif %S Astérisque %Z talk:603 %D 1983 %P 105-128 %N 105-106 %I Société mathématique de France %U http://archive.numdam.org/item/SB_1982-1983__25__105_0/ %G fr %F SB_1982-1983__25__105_0
Berestycki, Henri. Solutions périodiques de systèmes hamiltoniens, dans Séminaire Bourbaki : volume 1982/83, exposés 597-614, Astérisque, no. 105-106 (1983), Exposé no. 603, 24 p. http://archive.numdam.org/item/SB_1982-1983__25__105_0/
[1] Foundations of Mechanics, 2nd edition, Benjamin, New York (1967). | Zbl
, -[2] 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] Periodic solutions of asymptotically linear hamiltonian systems, Manuscripta Math. 32(1980), 149-189. | MR | Zbl
, -[4] On a theorem by Ekeland and Lasry concerning the number of periodic hamiltonian trajectories, J. Diff. Equ. 43(1981), 1-6. | Zbl
, -[5] Solutions of minimal period for a class of convex hamiltonian systems, Preprint. | MR
, -[6] Dual variational methods in critical point theory and applications, J. Funct. Anal. 14(1973), 349-381. | MR | Zbl
, -[7] Méthodes mathématiques de la mécanique classique, Editions Mir, Moscou (1976). | MR | Zbl
-[8] Problèmes ergodiques de la mécanique classique, Gauthier-Villars, Paris (1967). | MR | Zbl
, -[9] Variational principles for differential equations of elliptic, parabolic and hyperbolic type, Cahiers CEREMADE n° 7912, Univ. Paris-Dauphine. | Zbl
-[10] Second order evolution equations associated with convex hamiltonians, Bull. Canad. Math. (1979). | MR | Zbl
, -[11] Variational solutions of some nonlinear free boundary problems, Arch. Ration. Mech. Anal. 43(1971), 255-271. | MR | Zbl
, -[12] Groupes d'homotopie des ensembles de niveaux pour certaines fonctionnelles à gradient Fredholm, à paraître.
-[13] Forced vibrations of superquadratic hamiltonian systems, Acta Math. (1983), sous presse. | MR | Zbl
, -[14] Existence of forced oscillations for some nonlinear differential equations, Comm. Pure Applied Math. (1983), sous presse. | MR | Zbl
, -[15] Some critical point theorems and applications, Comm. Pure Applied Math. 33(1980), 147-172. | MR | Zbl
-[16] On critical point theory for indefinite functionals in the presence of symmetries, Trans. Amer. Math. Soc. 274(1982), 533-572. | MR | Zbl
-[17] 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] Critical point theorems for indefinite functionals, Invent. Math. 52(1979), 241-273. | MR | Zbl
, -[19] Orbites périodiques de systèmes conservatifs, Sém. Goulaouic-Meyer-Schwartz, Exposé n° XXIV, 1981-82, Ec. Polytechnique, Palaiseau. | Numdam | MR | Zbl
-[20] On a free boundary problem arising in plasma physics, Nonlinear Analysis, T.M.A. 4(1980), 415-436. | MR | Zbl
, -[21] A topological method for the existence of periodic orbits to conservative systems, Preprint.
, -[22] Existence of multiple periodic orbits on star-shaped hamiltonian surfaces, Preprint. | MR
, , , -[23] Nonlinearity and functional analysis, Academic Press, New York (1987). | MR | Zbl
-[24] On a family of periodic solutions for hamiltonian systems, J. Diff. Equ. 10(1971), 324-335. | MR | Zbl
-[25] Periodic solutions of nonlinear vibrating strings and duality principle, Bull. A.M.S., à paraître. | Zbl
-[26] Periodic solutions of nonlinear wave equations and hamiltonian systems, Amer. J. of Math. 103(1980), 559-570. | MR | Zbl
, -[27] Free vibrations for a nonlinear wave equation and a theorem of P. Rabinowitz, Comm. Pure Appl. Math. 33(1980), 667-684. | MR | Zbl
, , -[28] Un principe variationnel associé à certaines équations paraboliques, C.R.A.S. 282(1976), 971-974 et 1197-1198. | Zbl
, -[29] Solutions of asymptotically linear operator equations via Morse theory, Comm. Pure Appl. Math. 34(1981), 639-712. | MR | Zbl
-[30] A classical variational principle for periodic hamiltonian trajectories, Proc. Amer. Math. Soc. 76(1979), 186-188. | MR | Zbl
-[31] Periodic solutions to hamiltonian inclusions, J. Diff. Equ. 40(1981), 1-6. | MR | Zbl
-[32] Hamiltonian trajectories having prescribed minimal period, Comm. Pure Appl. Math. 33(1980), 103-116. | MR | Zbl
, -[33] 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] Morse type index theory for flows and periodic solutions for hamiltonian equations, à paraître. | Zbl
, -[35] The Birkhoff-Lewis fixed point theorem and a conjecture of V.I. Arnold, Version préliminaire.
, -[36] 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] Periodic solutions of hamiltonian equations and a theorem of P. Rabinowitz, J. Diff. Equ. 34(1979), 523-534. | MR | Zbl
-[38] Oscillations de systèmes hamiltoniens non linéaires III, Bull. Soc. Math. France 109(1981), 297-330. | Numdam | MR | Zbl
-[38B] Forced oscillations of nonlinear hamiltonian systems II, Advances Math. 7A(1981), 345-360. | MR | Zbl
-[39] A perturbation theory near convex hamiltonian systems, Cahiers CEREMADE n° 8226, Univ. Paris-Dauphine, à paraître. | Zbl
-[40] 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] On the number of periodic trajectories for a hamiltonian flow on a convex energy surface, Ann. Math. 112(1980), 283-319. | MR | Zbl
, -[42] Problèmes variationnels non convexes en dualité, C.R.A.S. Paris, Série A 291(1980), 493-496. | MR | Zbl
, -[43] Convex analysis and variational problems, North Holland, New York (1976). | MR | Zbl
, -[44] 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] Borsuk-Ulam theorem for arbitrary S1-actions and applications, MRC Report 2301, Madison Wis. USA.
, , -[45B] Some results on solutions of minimal period to superquadratic hamiltonian systems, Preprint. | MR
, -[46] A theorem on the existence of periodic solutions to hamiltonian systems with convex potentials, J. Diff. Equ. 10(1971), 324-335. | MR | Zbl
-[47] 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] The equivariant J-homomorphism for arbitrary S1-action, Preprint.
-[48] Méthodes topologiques dans les problèmes variationnals, Hermann, Paris (1934). | Zbl
, -[49] Problème général de la stabilité des mouvements, Ann. Fac. Sci. Toulouse 2(1907), 203-474.
-[50] Problèmes aux limites non homogènes et applications, Dunod, Paris (1968). | Zbl
, -[51] Metodi perturbativi nella teoria di Morse, Boll. U.M.I. 11(1975), 1-32. | MR | Zbl
, -[52] Contractive mappings and periodically perturbed conservative systems, Arch. Math. 12(1976), 67-74. | MR | Zbl
-[53] Periodic orbits near an equilibrium and a theorem by A. Weinstein, Comm. Pure Appl. Math. 29(1976), 727-747. | MR | Zbl
-[54] Some minimax principles and their applications in nonlinear elliptic equations, J. Analyses Math. 37(1980), 248-275. | MR | Zbl
-[55] Comments on nonlinear problems, Proceed. Conf. Catania (Italie), septembre 1981. | MR
-[56] Variational and topological methods in nonlinear problems, Bull. Amer. Math. Soc. 4(1981), 267-302. | MR | Zbl
-[57] Les méthodes nouvelles de la mécanique céleste, Gauthier-Villars, Paris (1982). | JFM
-[58] 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] Variational methods for nonlinear eigenvalue problems, (CIME, Varenna 1974), Ediz. Cremonese, Rome (1974). | MR
-[60] Free vibrations for a semi-linear wave equation, Comm. Pure Appl. Math. 31(1978), 31-68. | MR | Zbl
-[61] Periodic solutions of hamiltonian systems, Comm. Pure Appl. Math. 31(1978), 157-184. | MR | Zbl
-[62] 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] Periodic solutions of hamiltonian systems : A survey, MRC Techn. Report n° 2154, Univ. Wisconsin-Madison (1980).
-[64] Subharmonic solutions of hamiltonian systems, Comm. Pure Math. 33(1980), 609-633. | MR | Zbl
-[65] Periodic solutions of large norm of hamiltonian systems, Preprint. | MR
-[66] Multiple critical points of perturbed symmetric functionals, Trans. Amer. Math. Soc. 272(1982), 753-769. | MR | Zbl
-[67] Periodischer bewegungen mechanischer systeme, Math. Zeit. 51(1948), 197-216. | MR | Zbl
-[68] Lectures on celestial mechanics, Springer-Verlag, New York (1971) ; Grundlehren Math. vol. 187. | MR | Zbl
, -[69] A class of nonlinear differential equations of second order in time, Nonlinear Analysis, T.M.A. 2(1978), 355-373. | MR | Zbl
-[70] Lagragian submanifolds and hamiltonian systems, Ann. Math. 98 (1973), 377-410. | MR | Zbl
-[71] Normal modes for nonlinear hamiltonian systems, Invent. Math. 20 (1973), 47-57. | MR | Zbl
-[72] Periodic orbits for convex hamiltonian systems, Ann. Math. 108 (1987), 507-518. | MR | Zbl
-[73] Bifurcations and Hamilton's principle, Math. Zeit. 159(1978), 235-248. | MR | Zbl
-[74] On the hypotheses of Rabinowitz' periodic orbit theorems, J. Diff. Equ. 33(1979), 353-358. | MR | Zbl
-[75] Subharmonic oscillations of convex hamiltonian systems, Preprint. | MR
-[76] Subharmonic oscillations of nonlinear systems, Proceed. Conf. "Equa. diff. 82", Würzburg, à paraître. | Zbl
-