La dynamique au voisinage d'un point fixe elliptique conservatif : de Poincaré et Birkhoff à Aubry et Mather
Séminaire Bourbaki : volume 1983/84, exposés 615-632, Astérisque, no. 121-122 (1985), Exposé no. 622, 24 p.

Voir la notice du chapitre de livre provenant de la source Numdam

MR   Zbl   EuDML

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://geodesic.mathdoc.fr/item/SB_1983-1984__26__147_0/
@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},
     year = {1985},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {121-122},
     mrnumber = {768958},
     zbl = {0582.58013},
     language = {fr},
     url = {http://geodesic.mathdoc.fr/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://geodesic.mathdoc.fr/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://geodesic.mathdoc.fr/item/SB_1983-1984__26__147_0/
%G fr
%F SB_1983-1984__26__147_0

[1] D. G. Aronson, M. A. Chory, R. G. Hall and R. P. Mcgehee - 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. | Zbl | MR

[2] S. Aubry, P. Y. Le Daeron and G. André - Classical ground-states of a one-dimensional model for incommensurate structures, soumis à Communications in Math. Physics.

[3] G. D. Birkhoff - Proof of Poincaré's geometric theorem, Trans. Amer. Math. Soc. vol. 14(january 1913), 14-22. | JFM

[4] G. D. Birkhoff - An extension of Poincaré's last geometric theorem, Acta Math. (december 1925), 297-311. | JFM

[5] G. D. Birkhoff - Surface transformations and their dynamical applications, Acta math. vol. 43(march 1920), 1-119. | MR | JFM

[6] G. D. Birkhoff - On the periodic motions of dynamical systems, Acta Math. vol. 50(october 1927), 359-379. | MR | JFM

[7] G. D. Birkhoff and D. C. Lewis - On the periodic motions near a given Periodic Motion of a Dynamical System, Annali Matem. S-4, vol. 12(1933), 117-133. | JFM

[8] M. Chaperon - 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. | Zbl | MR | Numdam

[9] C. Conley and E. Zehnder - The Birkhoff-Lewis fixed point theorem and a Conjecture of V.I. Arnold, Inventiones Math. 73(1983), 33-49. | Zbl | MR

[10] Raph Douady - Application du théorème des tores invariants, Thèse de 3e cycle, Université de Paris 7, 1982.

[11] D. Goroff - Hyperbolic sets for twist maps, preprint 1983, soumis à Ergodic theory and dynamical systems. | Zbl | MR

[12] D. Goroff - A variational study of twist maps, en préparation.

[ 13] G. R. Hall - Bifurcation of an attracting invariant circle : A Denjoy attractor, Ergodic theory and dynamical systems, | Zbl | MR

[14] G. R. Hall - A topological version of a theorem of Mather on twist maps, preprint University of Wisconsin-Madison, 1983. | MR

[15] M. R. Herman - Sur la conjugaison différentiable des difféomorphismes du cercle à des rotations, Publ. I.H.E.S. 49(1979), 5-233. | Zbl | MR | Numdam

[16] M. R. Herman - Sur les courbes invariantes par les difféomorphismes de l'anneau, Volume 1, Astérisque n° 103-104, 1983. | Zbl | Numdam

[17] M. R. Herman - Sur les courbes invariantes par les difféomorphismes de l'anneau, Volume 2, soumis à Astérisque. | Zbl | Numdam

[18] M. R. Herman - Remarque sur les Cantors de Mather et Aubry, Conférence au Séminaire de l'École Polytechnique, 15/03/1982.

[19] M. R. Herman - Cantors hyperboliques, Conférence au Séminaire de l'École Polytechnique, 14/02/1983.

[20] A. Katok - Some remarks on Birkhoff and Mather twist map theorems, Ergodic theory and dynamical systems vol. 2(1982), 185-194. | Zbl | MR

[21] A. Katok - More about Birkhoff periodic orbits and Mather sets for twist maps, preprint I.H.E.S., 1982.

[22] R. S. Mackay, J. D. Meiss and I. C. Percival - Transport in Hamiltonian systems, preprint 1983, submitted to Physica D. | Zbl | MR

[ 23] L. Markus and K. R. Meyer - Periodic orbits and solenoids in generic hamiltonian dynamical systems, Amer. J. of Math. vol. 102(1980), 25-92. | Zbl | MR

[24] J. N. Mather - Existence of quasi-periodic orbits for twist homeomorphisms of the annulus, Topology vol. 21, n° 4(1982), 457-467. | Zbl | MR

[25] J. N. Mather - Concavity of the Lagrangian for quasi-periodic orbits, Comment. Math. Helvetici 57(1982), 356-376. | Zbl | MR

[26] J. N. Mather - Non-Uniqueness of Solutions of Percival's Euler-Lagrange Equations, Commun. Math. Phys. 86(1982), 465-473. | Zbl | MR

[27] J. N. Mather - A criterion for the Non-Existence of Invariant Circles, preprint, 1982.

[28] J. Moser - Non existence of Integrals for Canonical systems of Differential equations, Commun. on Pure and Appl. Math. vol. VIII(1955), 409-436. | Zbl | MR

[29] J. Moser - On invariant curves of area-preserving mappings of an annulus, Nachr. Akad. Wiss., Göttingen Math. Phys. K1 11(1962), 1-20. | Zbl | MR

[30] J. Moser - Stable and random motions in dynamical systems, Annals of Math. Studies 77, Princeton Univ. Press, Princeton N.J., 1973. | Zbl | MR

[31] J. Moser - Proof of a generalized form of a fixed point theorem due to G.D. Birkhoff, Lect. Notes in Math. 597, Springer-Verlag, 1977. | Zbl | MR

[32] I. C. Percival - 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] J. Poeschel - Integrability of hamiltonian systems on Cantor sets, Commun. Pure and Appl. Math. vol. 35(1982). | Zbl | MR

[34] H. Poincaré - Sur un théorème de géométrie, Rendiconti del Circolo Matematico di Palermo vol. 33(1912), 375-407. | JFM

[35] H. Poincaré - Les méthodes nouvelles de la Mécanique Céleste, Tome III, Gauthier-Villars, 1899. | JFM

[36] R. C. Robinson - Generic properties of conservative systems, Amer. J. Math. 92 (1970), 562-603. | Zbl | MR

[37] H. Rüssmann - On the existence of invariant curves of twist mapping of an annulus, Lect. Notes in Math. 1007, Springer-Verlag, 1983. | Zbl | MR

[38] F. Takens - A C1 counter-example to Moser's twist theorem, Indag. Math. 33(1971), 379-386. | Zbl | MR

[39] R. Thom - Travaux de Moser sur la stabilité des mouvements périodiques, Séminaire Bourbaki 1963-64, exp. 264, W.A. Benjamin Inc., 1966. | Zbl | MR | Numdam

[40] E. Zehnder - Homoclinic Points near Elliptic Fixed Points, Commun. on Pure and Appl. Math. vol. XXVI(1973), 131-182. | Zbl | MR

[41] M. Morse - A fundamental class of geodesics on any closed surface of genus greater than one, Transactions A.M.S. vol. 26(1924), 25-60. | MR | JFM

[42] G. Hedlund - Geodesics on a 2-dimensional riemannian manifold with periodic coefficients, Annals of Math. serie II vol. 33(1932), 719-739. | MR | JFM