@incollection{SB_1983-1984__26__147_0, author = {Chenciner, Alain}, title = {La dynamique au voisinage d'un point fixe elliptique conservatif : de {Poincar\'e} et {Birkhoff} \`a {Aubry} et {Mather}}, booktitle = {S\'eminaire Bourbaki : volume 1983/84, expos\'es 615-632}, series = {Ast\'erisque}, note = {talk:622}, pages = {147--170}, publisher = {Soci\'et\'e math\'ematique de France}, number = {121-122}, year = {1985}, mrnumber = {768958}, zbl = {0582.58013}, language = {fr}, url = {http://www.numdam.org/item/SB_1983-1984__26__147_0/} }
TY - CHAP AU - Chenciner, Alain TI - La dynamique au voisinage d'un point fixe elliptique conservatif : de Poincaré et Birkhoff à Aubry et Mather BT - Séminaire Bourbaki : volume 1983/84, exposés 615-632 AU - Collectif T3 - Astérisque N1 - talk:622 PY - 1985 SP - 147 EP - 170 IS - 121-122 PB - Société mathématique de France UR - http://www.numdam.org/item/SB_1983-1984__26__147_0/ LA - fr ID - SB_1983-1984__26__147_0 ER -
%0 Book Section %A Chenciner, Alain %T La dynamique au voisinage d'un point fixe elliptique conservatif : de Poincaré et Birkhoff à Aubry et Mather %B Séminaire Bourbaki : volume 1983/84, exposés 615-632 %A Collectif %S Astérisque %Z talk:622 %D 1985 %P 147-170 %N 121-122 %I Société mathématique de France %U http://www.numdam.org/item/SB_1983-1984__26__147_0/ %G fr %F SB_1983-1984__26__147_0
Chenciner, Alain. La dynamique au voisinage d'un point fixe elliptique conservatif : de Poincaré et Birkhoff à Aubry et Mather, dans Séminaire Bourbaki : volume 1983/84, exposés 615-632, Astérisque, no. 121-122 (1985), Exposé no. 622, 24 p. http://www.numdam.org/item/SB_1983-1984__26__147_0/
[1] Bifurcations from an Invariant Circle for Two-Parameter families of Maps of the Plane : A computer-Assisted study, Communications in Math. Physics 83(1982), 303-354. | MR | Zbl
, , and -[2] Classical ground-states of a one-dimensional model for incommensurate structures, soumis à Communications in Math. Physics.
, and -[3] Proof of Poincaré's geometric theorem, Trans. Amer. Math. Soc. vol. 14(january 1913), 14-22. | JFM
-[4] An extension of Poincaré's last geometric theorem, Acta Math. (december 1925), 297-311. | JFM
-[5] Surface transformations and their dynamical applications, Acta math. vol. 43(march 1920), 1-119. | JFM | MR
-[6] On the periodic motions of dynamical systems, Acta Math. vol. 50(october 1927), 359-379. | JFM | MR
-[7] On the periodic motions near a given Periodic Motion of a Dynamical System, Annali Matem. S-4, vol. 12(1933), 117-133. | JFM
and -[8] Quelques questions de géométrie symplectique [d'après entre autres, Poincaré, Arnold, Conley et Zehnder], Séminaire Bourbaki 1982-83, exp. n° 610, Astérisque 105-106(1983), 231-249. | Numdam | MR | Zbl
-[9] The Birkhoff-Lewis fixed point theorem and a Conjecture of V.I. Arnold, Inventiones Math. 73(1983), 33-49. | MR | Zbl
and -[10] Application du théorème des tores invariants, Thèse de 3e cycle, Université de Paris 7, 1982.
-[11] Hyperbolic sets for twist maps, preprint 1983, soumis à Ergodic theory and dynamical systems. | MR | Zbl
-[12] A variational study of twist maps, en préparation.
-[ 13] Bifurcation of an attracting invariant circle : A Denjoy attractor, Ergodic theory and dynamical systems, | MR | Zbl
-[14] A topological version of a theorem of Mather on twist maps, preprint University of Wisconsin-Madison, 1983. | MR
-[15] Sur la conjugaison différentiable des difféomorphismes du cercle à des rotations, Publ. I.H.E.S. 49(1979), 5-233. | Numdam | MR | Zbl
-[16] Sur les courbes invariantes par les difféomorphismes de l'anneau, Volume 1, Astérisque n° 103-104, 1983. | Numdam | Zbl
-[17] Sur les courbes invariantes par les difféomorphismes de l'anneau, Volume 2, soumis à Astérisque. | Numdam | Zbl
-[18] Remarque sur les Cantors de Mather et Aubry, Conférence au Séminaire de l'École Polytechnique, 15/03/1982.
-[19] Cantors hyperboliques, Conférence au Séminaire de l'École Polytechnique, 14/02/1983.
-[20] Some remarks on Birkhoff and Mather twist map theorems, Ergodic theory and dynamical systems vol. 2(1982), 185-194. | MR | Zbl
-[21] More about Birkhoff periodic orbits and Mather sets for twist maps, preprint I.H.E.S., 1982.
-[22] Transport in Hamiltonian systems, preprint 1983, submitted to Physica D. | MR | Zbl
, and -[ 23] Periodic orbits and solenoids in generic hamiltonian dynamical systems, Amer. J. of Math. vol. 102(1980), 25-92. | MR | Zbl
and -[24] Existence of quasi-periodic orbits for twist homeomorphisms of the annulus, Topology vol. 21, n° 4(1982), 457-467. | MR | Zbl
-[25] Concavity of the Lagrangian for quasi-periodic orbits, Comment. Math. Helvetici 57(1982), 356-376. | MR | Zbl
-[26] Non-Uniqueness of Solutions of Percival's Euler-Lagrange Equations, Commun. Math. Phys. 86(1982), 465-473. | MR | Zbl
-[27] A criterion for the Non-Existence of Invariant Circles, preprint, 1982.
-[28] Non existence of Integrals for Canonical systems of Differential equations, Commun. on Pure and Appl. Math. vol. VIII(1955), 409-436. | MR | Zbl
-[29] On invariant curves of area-preserving mappings of an annulus, Nachr. Akad. Wiss., Göttingen Math. Phys. K1 11(1962), 1-20. | MR | Zbl
-[30] Stable and random motions in dynamical systems, Annals of Math. Studies 77, Princeton Univ. Press, Princeton N.J., 1973. | MR | Zbl
-[31] Proof of a generalized form of a fixed point theorem due to G.D. Birkhoff, Lect. Notes in Math. 597, Springer-Verlag, 1977. | MR | Zbl
-[32] Variational principles for invariant tori and cantori, in Symp. on Nonlinear Dynamics and Beam-Beam Interactions, edited by M. Mouth and J.C. Herrava, n° 57, Amer. Instit. of Physics, Conf. Proc. (1980), 310-320. | MR
-[33] Integrability of hamiltonian systems on Cantor sets, Commun. Pure and Appl. Math. vol. 35(1982). | MR | Zbl
-[34] Sur un théorème de géométrie, Rendiconti del Circolo Matematico di Palermo vol. 33(1912), 375-407. | JFM
-[35] Les méthodes nouvelles de la Mécanique Céleste, Tome III, Gauthier-Villars, 1899. | JFM
-[36] Generic properties of conservative systems, Amer. J. Math. 92 (1970), 562-603. | MR | Zbl
-[37] On the existence of invariant curves of twist mapping of an annulus, Lect. Notes in Math. 1007, Springer-Verlag, 1983. | MR | Zbl
-[38] A C1 counter-example to Moser's twist theorem, Indag. Math. 33(1971), 379-386. | MR | Zbl
-[39] Travaux de Moser sur la stabilité des mouvements périodiques, Séminaire Bourbaki 1963-64, exp. 264, W.A. Benjamin Inc., 1966. | Numdam | MR | Zbl
-[40] Homoclinic Points near Elliptic Fixed Points, Commun. on Pure and Appl. Math. vol. XXVI(1973), 131-182. | MR | Zbl
-[41] A fundamental class of geodesics on any closed surface of genus greater than one, Transactions A.M.S. vol. 26(1924), 25-60. | JFM | MR
-[42] Geodesics on a 2-dimensional riemannian manifold with periodic coefficients, Annals of Math. serie II vol. 33(1932), 719-739. | JFM | MR
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