@incollection{XUPS_1994____93_0, author = {Patrice Le Calvez}, title = {Du billard convexe aux~g\'eod\'esiques~du~tore}, booktitle = {Aspects des syst\`emes dynamiques (des \'equations diff\'erentielles aux it\'erations de fonctions)}, series = {Journ\'ees math\'ematiques X-UPS}, pages = {93--140}, publisher = {Les \'Editions de l{\textquoteright}\'Ecole polytechnique}, year = {1994}, doi = {10.5802/xups.1994-04}, language = {fr}, url = {https://proceedings.centre-mersenne.org/articles/10.5802/xups.1994-04/} }
TY - JOUR AU - Patrice Le Calvez TI - Du billard convexe aux géodésiques du tore JO - Journées mathématiques X-UPS PY - 1994 SP - 93 EP - 140 PB - Les Éditions de l’École polytechnique UR - https://proceedings.centre-mersenne.org/articles/10.5802/xups.1994-04/ DO - 10.5802/xups.1994-04 LA - fr ID - XUPS_1994____93_0 ER -
%0 Journal Article %A Patrice Le Calvez %T Du billard convexe aux géodésiques du tore %J Journées mathématiques X-UPS %D 1994 %P 93-140 %I Les Éditions de l’École polytechnique %U https://proceedings.centre-mersenne.org/articles/10.5802/xups.1994-04/ %R 10.5802/xups.1994-04 %G fr %F XUPS_1994____93_0
Patrice Le Calvez. Du billard convexe aux géodésiques du tore. Journées mathématiques X-UPS (1994), pp. 93-140. doi : 10.5802/xups.1994-04. https://proceedings.centre-mersenne.org/articles/10.5802/xups.1994-04/
[1] S. Aubry; P. Y. Le Daeron The discrete Frenkel-Kontorova model and its generalizations, Physica, Volume 8D (1983), pp. 381-422 | Zbl
[2] V. Bangert Mather sets for twist maps and geodesics on tori, Dynamics reported, Vol. 1 (Dynam. Report. Ser. Dynam. Systems Appl.), Volume 1, Wiley, Chichester, 1988, pp. 1-56 | DOI | MR | Zbl
[3] V. Bangert Minimal geodesics, Ergod. Th. Dynam. Sys., Volume 10 (1989), pp. 263-286 | DOI | MR
[4] D. Bernstein; A. Katok Birkhoff periodic orbits for small perturbations of completely integrable Hamiltonian systems with convex Hamiltonians, Invent. Math., Volume 88 (1987), pp. 225-241 | DOI | MR | Zbl
[5] G. D. Birkhoff Surface transformations and their dynamical applications, Acta Math., Volume 43 (1920), pp. 1-119 | DOI | MR | Zbl
[6] G. D. Birkhoff On the periodic motions of dynamical systems, Acta. Math., Volume 50 (1927), pp. 359-379 | DOI | MR | Zbl
[7] G. D. Birkhoff Sur quelques courbes fermées remarquables, Bull. Soc. Math. France, Volume 80 (1932), pp. 1-26 | Numdam | Zbl
[8] A. Chenciner La dynamique au voisinage d’un point fixe elliptique conservatif : de Poincaré et Birkhoff à Aubry et Mather, Séminaire Bourbaki (Astérisque), Société Mathématique de France, Paris, 1985, pp. 165-173 (Exp. no. 622) | Numdam | Zbl
[9] R. Douady Application du théorème des tores invariants, Thèse de troisième cycle, Univ. Paris VII (1982)
[10] G. A. Hedlund Geodesics on a two-dimensional Riemannian manifold with periodic coefficients, Ann. of Math., Volume 33 (1932), pp. 719-739 | DOI | MR | Zbl
[11] M. R. Herman Sur les courbes invariantes par les difféomorphismes de l’anneau, Astérisque, 103-104, Société Mathématique de France, Paris, 1983 | Numdam
[12] M. R. Herman Inégalités a priori pour des tores lagrangiens invariants par des difféomorphismes symplectiques, Publ. Math. I.H.E.S., Volume 70 (1989), pp. 47-101 | DOI | Numdam | Zbl
[13] A. Katok Some remarks on Birkhoff and Mather twist map theorem, Ergod. Th. Dynam. Sys., Volume 2 (1982), pp. 185-194 | DOI | MR | Zbl
[14] V. F. Lazutkin Concerning a theorem of Moser on invariant curves, Probl. Dyn. Theory Propag. Seism. Waves, Volume 14 (1974), pp. 109-120
[15] J. Mather Existence of quasi-periodic orbits for twist homeomorphisms of the annulus, Topology, Volume 21 (1982), pp. 457-467 | DOI | Zbl
[16] J. Mather Glancing Billards, Ergod. Th. Dynam. Sys., Volume 2 (1982), p. 597-403 | DOI | Zbl
[17] J. Mather A criterion for the non-existence of invariant circles, Publ. Math. I.H.E.S., Volume 63 (1986), pp. 153-204 | DOI | Numdam | MR | Zbl
[18] J. Mather Minimal action measures for positive definite Lagrangian systems, IXth International Congress on Mathematical Physics (Swansea, 1988), Hilger, Bristol, 1989, pp. 466-468 | MR | Zbl
[19] J. Mather Minimal measures, Comment. Math. Helv., Volume 64 (1989), pp. 375-394 | DOI | MR | Zbl
[20] M. Morse A fundamental class of geodesics on any closed surface of genus greater than one, Trans. Am. Math. Soc., Volume 26 (1924), pp. 25-60 | DOI | MR | Zbl
[21] J. Moser Monotone twist mappings and the calculus of variation, Ergod. Th. Dynam. Sys., Volume 6 (1986), pp. 401-413 | DOI | MR | Zbl
[22] J. Moser Recent developments in the theory of Hamiltonian systems, SIAM Review, Volume 8 (1986), pp. 459-485 | MR | Zbl
Cité par Sources :