@incollection{SB_1984-1985__27__113_0, author = {Bost, Jean-Beno{\^\i}t}, title = {Tores invariants des syst\`emes dynamiques hamiltoniens}, booktitle = {S\'eminaire Bourbaki : volume 1984/85, expos\'es 633-650}, series = {Ast\'erisque}, note = {talk:639}, pages = {113--157}, publisher = {Soci\'et\'e math\'ematique de France}, number = {133-134}, year = {1986}, mrnumber = {837218}, zbl = {0602.58021}, language = {fr}, url = {http://archive.numdam.org/item/SB_1984-1985__27__113_0/} }
TY - CHAP AU - Bost, Jean-Benoît TI - Tores invariants des systèmes dynamiques hamiltoniens BT - Séminaire Bourbaki : volume 1984/85, exposés 633-650 AU - Collectif T3 - Astérisque N1 - talk:639 PY - 1986 SP - 113 EP - 157 IS - 133-134 PB - Société mathématique de France UR - http://archive.numdam.org/item/SB_1984-1985__27__113_0/ LA - fr ID - SB_1984-1985__27__113_0 ER -
%0 Book Section %A Bost, Jean-Benoît %T Tores invariants des systèmes dynamiques hamiltoniens %B Séminaire Bourbaki : volume 1984/85, exposés 633-650 %A Collectif %S Astérisque %Z talk:639 %D 1986 %P 113-157 %N 133-134 %I Société mathématique de France %U http://archive.numdam.org/item/SB_1984-1985__27__113_0/ %G fr %F SB_1984-1985__27__113_0
Bost, Jean-Benoît. Tores invariants des systèmes dynamiques hamiltoniens, dans Séminaire Bourbaki : volume 1984/85, exposés 633-650, Astérisque, no. 133-134 (1986), Exposé no. 639, 45 p. http://archive.numdam.org/item/SB_1984-1985__27__113_0/
[1] Foundations of Mechanics, 2nd ed., Benjamin/ Cummings, Reading, Mass., 1978. | MR | Zbl
and -[2] Méthodes mathématiques de la mécanique classique, MIR, Moscou, 1974. | MR | Zbl
-[3] Vorlesungen über Dynamik, Gesammelte Werke, VIII (Supplementband), Berlin, 1884 - Chelsea, New York, 1969.
-[4] Les méthodes nouvelles de la mécanique céleste, 3 vol., Gauthier-Villars, Paris, 1892-1899. | JFM
-[5] A treatise on the analytical dynamics of particles and rigid bodies, 4th ed., Cambridge Univ. Press, Cambridge, 1959. | MR | Zbl
-[6] Dynamical systems, Colloq. Publ. IX, 2nd ed., Amer. Math. Soc., Providence, R.I, 1966. | MR
-[7] Integrability and non-integrability in Hamiltonian mechanics, Russian Math. Surveys 38:1(1983), 1-76. | MR | Zbl
-[8] Various aspects of integrable Hamiltonian systems, Progress in Math. 8, Birkhäuser, Boston (1980), 233-289. | MR | Zbl
-[9] Small denominators I. On the mapping of a circle into itself, Transl. Amer. Math. Soc. serie 2, 46(1965), 213-284. | Zbl
-[10] Small denominators II. Proof of a theorem of A. N. Kolmogorov on the invariance of quasi-periodic motion under small perturbations of the Hamiltonian, Russian Math. Surveys 18, n° 5(1963), 9-36. | MR | Zbl
-[11] Small denominators III. Small denominators and problems of stability of motion in classical and celestial mechanics, Russian Math. Surveys 18, n° 6(1963), 85-193. | MR | Zbl
-[12] Chapitres supplémentaires de la théorie des équations différentielles ordinaires, MIR, Moscou, 1978. | MR | Zbl
-[13] Problèmes ergodiques de la mécanique classique, Gauthier-Villars, Paris, 1967. | MR | Zbl
et -[14] A metal-insulator transition for the almost Mathieu model, Comm. Math. Phys. 88(1983), 207-234. | MR | Zbl
, and -[15] La dynamique au voisinage d'un point fixe elliptique conservatif : de Poincaré et Birkhoff à Aubry et Mather, Séminaire Bourbaki 1983-84, n° 622, Astérisque 121-122(1985), 147-170. | Numdam | MR | Zbl
-[16] Bifurcations de points fixes elliptiques, preprint Université Paris 7 (1984), à paraître aux Publ. Math. IHES. | Numdam | Zbl
-[17] Smooth prime integrals for quasi-integrable Hamiltonian systems, Il Nuovo Cimento 67B(1982), 277-295. | MR
and -[18] Quasi-modes sur les variétés riemanniennes, Invent. Math. 43(1977), 15-52. | MR | Zbl
-[19] The one-dimensional Schrödinger equation with a quasi-periodic potential, Funct. Anal. Appl. 9 (1976) , 279-289. | Zbl
and -[20] Applications du théorème des tores invariants, Thèse de 3e cycle, Université Paris 7 (juin 1982).
-[21] Une démonstration directe de l'équivalence des théorèmes de tores invariants pour difféomorphismes et champs de vecteurs, C.R. Acad. Sci. Paris 295(1982), 201-204. | MR | Zbl
-[22] Exemple de point fixe elliptique non stable en dimension 4, C.R. Acad. Sci. Paris 296 (1983) , 895-898. | MR | Zbl
et -[23] On the continuation of hyperbolic invariant tori for Hamiltonian systems, Jour. of Diff. Equ. 15 (1974) , 1-69. | MR | Zbl
-[24] Sur le groupe des difféomorphismes du tore, Ann. de l'Institut Fourier 23(2) (1973), 75-86. | Numdam | MR | Zbl
-[25] Résultats récents sur la conjugaison différentiable, Proc. of the Internat. Congress of Mathematicians, Helsinki (1978), 811-820. | MR | Zbl
-[26] Sur la conjugaison différentiable des difféomorphismes du cercle à des rotations, Publ. Math. IHES 49(1979), 5-234. | Numdam | MR | Zbl
-[27] Démonstration du théorème des courbes translatées par les difféomorphismes de l'anneau ; démonstration du théorème des tores invariants, manuscrit (1980).
-[28] Une méthode pour minorer les exposants de Lyapounov, Preprint Centre de Math. de l'École Polytechnique (1982).
-[29] Sur les courbes invariantes par les difféomorphismes de l'anneau, Volume I : Astérisque 103-104 (1983) ; Volume II : Preprint Centre de Math. de l'Ecole Polytechnique, à paraître chez Astérisque. | Numdam | Zbl
-[30] Exemples de fractions rationnelles ayant une orbite dense sur la sphère de Riemann, Bull. Soc. Math. France 112(1984), 93-142. | Numdam | MR | Zbl
-[31] Simple proof of local conjugacy theorems for diffeomorphisms of the circle with almost every rotation number, Preprint, MSRI, Berkeley (1984). | MR
-[32] Sur la conservation des orbites quasi-périodiques lors d' une petite perturbation du hamiltonien, (en russe), Dokl. Akad. Nauk 98 n° 4(1954), 527-530. | Zbl
-[33] Théorie générale des systèmes dynamiques et mécanique classique, (en russe), Proc. of the 1954 Intern. Congress, North Holland, Amsterdam, V1 315-333. Traduction anglaise dans [1], 741-757. | MR | Zbl
-[34] The existence of caustics for a billiard problem in a convex domain, Math. USSR Izvestija 7(1973), 185-214. | Zbl
-[35] Existence of quasiperiodic solutions in the Three-Body-Problem, Celestial Mechanics 3(1971), 408-426. | MR | Zbl
-[36] Quasiperiodic solutions of Hamiltonian systems, Jour. of Diff. Equ. 11(1972), 109-137. | MR | Zbl
-[37] Generic Hamiltonian systems are neither integrable nor ergodic, Memoirs of the Amer. Math. Soc. 144 (1974) . | MR | Zbl
and -[38] Normalisation des champs de vecteurs holomorphes (d'après A.D. Brjuno), Séminaire Bourbaki 1980-81, n° 564, Springer-Verlag, Lect. Notes in Math. 901(1981), 55-70. | Numdam | MR | Zbl
-[39] On invariant curves of area-preserving mappings of an annulus, Nachr. Akad. Wiss. Göttingen, Math. Phys. Kl. (1962), 1-20. | MR | Zbl
-[40] A rapidly convergent iteration method and nonlinear partial differential equations, Ann. Scuola Norm. Sup. Pisa 20(1966), I : 265-315, II : 499-535. | Numdam | Zbl
-[41] Convergent series expansions for quasi-periodic motions, Math. Ann. 169(1967), 136-176. | MR | Zbl
-[42] Lectures on Hamiltonian systems, Memoirs Amer. Math. Soc. 81(1968), 1-60. | MR | Zbl
-[43] On the construction of almost periodic solutions for ordinary differential equations, Proc. of the Internat. Conf. on Functional Analysis and Pelated Topics, Tokyo (1969), 60-67. | MR | Zbl
-[44] Stable and random motions in dynamical systems, Ann. Math. Studies n° 77, Princeton Univ. Press, Princeton N.J., 1973. | MR | Zbl
-[45] Is the solar system stable ?, Math. Intelligenoer 1(1978), 65-71. | MR
-[46] An extension of a result by Dinaburg and Sinai on quasiperiodic potential, Comment. Math. Helvetici 59 (1984) , 39-85. | MR | Zbl
and -[47] Über invariante Tori in differenzierbaren Hamiltonschen Systemen, Bonner Mathematische Schriften 120(1980). | MR | Zbl
-[48] Integrability of Hamiltonian systems on Cantor sets, Comm. Pure Appl. Math. 35(1982), 653-695. | MR | Zbl
-[49] Generic properties of conservative systems, Amer. J. of Math. 92(1970), I : 562-603, II : 897-906. | MR | Zbl
-[50] Kleine Nenner I : Über invarianten Kurven differenzierbarer Abbildungen eines Kreisringes, Nachr. Akad. Wiss. Göttingen, Math. Phys. K1. (1970), 67-105. | MR | Zbl
-[51] Kleine Nenner II : Bemerkungen zur Newtonschen Methode, Nachr. Akad. Wiss. Göttingen, Math. Phys. K1. (1972), 1-10. | MR | Zbl
-[52] On optimal estimates for the solutions of linear partial differential equations of first order with constant coefficients on the torus, Lect. Notes in Physics 38(1975), 598-624. | MR | Zbl
-[53] Note on sums containing small divisors, Comm. Pure Appl. Math. 29(1976), 755-758. | MR | Zbl
-[54] On the one-dimensional Schrödinger equation with a quasi-periodic potential, Ann. New York Acad. Sci. 357(1980), 90-107. | MR | Zbl
-[55] On the existence of invariant curves of twist mappings of an annulus, Lect. Notes in Math. 1007(1983), 677-712. | MR | Zbl
-[56] Iteration of analytic functions, Ann. of Math. 43 (1942) , 607- 612. | MR | Zbl
-[57] Über die analytische Normalform analytischer Differentialgleichungen in der Nähe einer Gleichgewichtslösung, Nachr. Akad. Wiss. Göttingen, Math. Phys. Kl. (1952), 21-30. | MR | Zbl
-[58] Lectures on Celestial Mechanics, Springer, Grundlehren Bd. 187(1971). | MR | Zbl
and -[59] Almost periodic Schrödinger operator : a review, Adv. Appl. Math. 3(1982), 463-490. | MR | Zbl
-[60] Small perturbations of an integrable dynamical system with an integral invariant, Proc. Steklov Inst. of Math. n° 2(1981) , 127-151. | MR | Zbl
-[61] Foliations and groups of diffeomorphisms, Bull. Amer. Math. Soc. 80(1974), 304-307. | MR | Zbl
-[62] Conjugaison différentiable des difféomorphismes du cercle dont le nombre de rotation vérifie une condition diophantienne, Ann. Sci. E.N.S. 4e s., 17(1984), 333-359. | Numdam | MR | Zbl
-[63] Generalized implicit function theorems with applications to some small divisor problems, Comm. Pure Appl. Math., I : 28(1975), 91-140, II: 29(1976), 49-113. | MR | Zbl
-[64] Smoothing and inversion of differential operators, Math. USSR Sbornik 17(1972), 381-434. | MR | Zbl
-[65] The inverse function theorem of Nash and Moser, Preprint, Cornell University, 1974. | MR
-[66] The inverse function theorem of Nash and Moser, Bull. Amer. Math. Soc. 7(1982), 65-222. | MR | Zbl
-[67] The boundary problem of physical geodesy, Arch. Rat. Mach. Anal. 62(1976), 1-52. | MR | Zbl
-[68] Implicit function theorems, Lectures at Stanford University, Summer Quarter 1977.
-[69] On the Nash-Moser implicit function theorem, Preprint. | MR
-[70] An inverse function theorem in Fréchet spaces, Jour. of Funct. Anal. 33(1979), 165-174. | MR | Zbl
and -[71] A new technique for the construction of solutions of non-linear differential equations, Proc. Nat. Acad. Sci. USA 47(1961), 1824-1831. | MR | Zbl
-[72] The embedding problem for Riemannian manifolds, Ann. of Math. 63 (1956), 20-63. | MR | Zbl
-[73] Un théorème de fonctions implicites sur certains espaces de Fréchet et quelques applications, Ann. Sci. E.N.S. 4e s., 5(1972), 599-660. | Numdam | MR | Zbl
-[74] Moser's implicit function theorem in the framework of analytic smoothing, Math. Annalen 219(1976), 105-121. | MR | Zbl
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