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Orbites périodiques des systèmes Hamiltoniens Autonomes [d'après Clarke, Ekeland-Lasry, Moser, Rabinowitz, Weinstein]

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Séminaire Bourbaki vol. 1979/80 Exposés 543 – 560

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Bibliographie

  1. R. ABRAHAM, J.E. MARSDEN-Foundations of Mechanics, 2nd edition, Benjamin.

    Google Scholar 

  2. H. AMANN, E. ZEHNDER-Non trivial solutions for a class of non resonance problems and applications to non linear differential equations, à paraître.

    Google Scholar 

  3. V.I. ARNOLD-Méthodes mathématiques de la mécanique classique, éditions Mir.

    Google Scholar 

  4. V.I. ARNOLD, A. AVEZ-Problèmes ergodiques de la mécanique classique, éditions Gauthier-Villars.

    Google Scholar 

  5. V. BENCI, P.H. RABINOWITZ-Critical point theorems for indefinite functionals, Inv. Math., Vol 52, fasc. 3(1979), p. 241–274.

    Article  MATH  MathSciNet  Google Scholar 

  6. M. BERGER-On a family of periodic solutions for Hamiltonian systems, J. Diff. Eq., 10(1971), p. 324–335.

    Article  Google Scholar 

  7. G.D. BIRKHOFF-On the periodic motions of dynamical systems, Acta Math., 50(1927), p. 359–379.

    Article  MATH  Google Scholar 

  8. D. CLARK-On periodic solutions of autonomous Hamiltonian systems of ordinary differential equations, Proc. A.M.S., 39(1973), p. 579–584.

    Article  MATH  Google Scholar 

  9. F.H. CLARKE-Periodic solutions to Hamiltonian inclusions, à paraître J. Diff. Eq.

    Google Scholar 

  10. F.H. CLARKE, I. EKELAND-Hamiltonian trajectories having prescribed minimal period, Preprint, cahier CEREMADE no 7822. Note C.R.A.S. t. 287(1978), p. 1013–1015. À paraître Comm. on pure and appl. Math..

    MATH  MathSciNet  Google Scholar 

  11. I. EKELAND-Periodic solutions of Hamiltonian equations and a theorem of P. Rabinowitz, J. Diff. Eq., Vol. 34, no 3 déc. 1979, p. 523–534.

    Article  MATH  MathSciNet  Google Scholar 

  12. I. EKELAND, J.M. LASRY-Nombre de solutions périodiques des équations de Hamilton, Preprint cahier CEREMADE no 7902, à paraître Annals of Math.

    Google Scholar 

  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.

    Article  MATH  Google Scholar 

  14. A.I. FET, L.A. LUSTERNIK-Variational problems on closed manifolds, Dokl. Akad. Nauk S.S.S.R., 81(1951), p. 17–18.

    MATH  Google Scholar 

  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.

    Article  MATH  Google Scholar 

  16. Y. HAGIHARA-Celestial Mechanics, Jap. Soc. for promotion of science, Tokyo 1975.

    Google Scholar 

  17. J. HORN-Beiträge zur Theorie der kleinen Schwingungen, Z. Math. Phys., 48(1903), p. 400–434.

    MATH  Google Scholar 

  18. W. KLINGENBERG-Closed geodesics, Grundlehren der Mathematischen Wissenschaften, Vol. 230, Springer 1978.

    Google Scholar 

  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.

    Google Scholar 

  20. L. LUSTERNIK, L. SCHNIRELMAN-Méthodes topologiques dans les problèmes variationnels, Hermann, Paris, 1934.

    MATH  Google Scholar 

  21. A. LYAPUNOV-Problème général de la stabilité des mouvements, Ann. Fac. Sci. de Toulouse, 2(1907), p. 203–474.

    Google Scholar 

  22. J. MOSER-A theorem by A. Weinstein and bifurcation theory, Report of the University Louvain la Neuve, Janv. 1976.

    Google Scholar 

  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.

    Google Scholar 

  24. J. MOSER-Proof of a generalized form of a fixed point theorem, Geometry and Topology, Rio de Janeiro, July 1976. Lecture Notes no 597, Springer, p. 464–494.

    Google Scholar 

  25. R.S. PALAIS-Critical point theory and the minimax principle, Global Analysis, Proc. A.M.S., Vol. XV, p. 185–212.

    Google Scholar 

  26. H. POINCARÉ-Les méthodes nouvelles de la mécanique céleste, Gauthier-Villars, 1892.

    Google Scholar 

  27. P.H. RABINOWITZ-Periodic solutions of Hamiltonian systems, Comm. pure and appl. Math., Vol. XXXI, 1978, p. 157–184.

    MathSciNet  Google Scholar 

  28. J.T. SCHWARTZ-Non linear functional analysis, Gordon and Breach 1969.

    Google Scholar 

  29. C.L. SIEGEL, J.K. MOSER-Lectures on celestial mechanics, Grundlehren des Math. Wiss., no 187, Springer 1971.

    Google Scholar 

  30. H. SEIFERT-Periodische Bewegungen mechanischer system, Math. Zeits. 51(1948), p. 197–216.

    Article  MATH  MathSciNet  Google Scholar 

  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.

    MATH  MathSciNet  Google Scholar 

  32. A. WEINSTEIN-Lagrangian submanifolds and hamiltonian systems, Ann. of Math., 98(1973), p. 377–410.

    Article  MATH  MathSciNet  Google Scholar 

  33. A. WEINSTEIN-Normal modes for non linear hamiltonian systems, Inv. Math., 20(1973), p. 47–57.

    Article  MATH  MathSciNet  Google Scholar 

  34. A. WEINSTEIN-Periodic orbits for convex hamiltonian systems, Ann. of Math., 108(1978), p. 507–518.

    Article  MATH  MathSciNet  Google Scholar 

  35. A. WEINSTEIN-Bifurcations and Hamilton's principle, Math. Zeits., 159(1978), p. 235–248.

    Article  MATH  MathSciNet  Google Scholar 

  36. A. WEINSTEIN-On the hypotheses of Rabinowitz' periodic orbit theorems, J. Diff. Eq., Vol. 33, no 3(1979), p. 353–358.

    Article  MATH  MathSciNet  Google Scholar 

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Desolneux-Moulis, N. (1981). Orbites périodiques des systèmes Hamiltoniens Autonomes [d'après Clarke, Ekeland-Lasry, Moser, Rabinowitz, Weinstein]. In: Séminaire Bourbaki vol. 1979/80 Exposés 543 – 560. Lecture Notes in Mathematics, vol 842. Springer, Berlin, Heidelberg . https://doi.org/10.1007/BFb0089933

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  • DOI: https://doi.org/10.1007/BFb0089933

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