Voir la notice de l'article provenant de la source Math-Net.Ru
@article{FAA_1986_20_4_a1, author = {M. L. Byalyi and L. V. Polterovich}, title = {Geodesic flows on the two-dimensional torus and phase transitions ``commensurability-noncommensurability''}, journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a}, pages = {9--16}, publisher = {mathdoc}, volume = {20}, number = {4}, year = {1986}, language = {ru}, url = {http://geodesic.mathdoc.fr/item/FAA_1986_20_4_a1/} }
TY - JOUR AU - M. L. Byalyi AU - L. V. Polterovich TI - Geodesic flows on the two-dimensional torus and phase transitions ``commensurability-noncommensurability'' JO - Funkcionalʹnyj analiz i ego priloženiâ PY - 1986 SP - 9 EP - 16 VL - 20 IS - 4 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/FAA_1986_20_4_a1/ LA - ru ID - FAA_1986_20_4_a1 ER -
%0 Journal Article %A M. L. Byalyi %A L. V. Polterovich %T Geodesic flows on the two-dimensional torus and phase transitions ``commensurability-noncommensurability'' %J Funkcionalʹnyj analiz i ego priloženiâ %D 1986 %P 9-16 %V 20 %N 4 %I mathdoc %U http://geodesic.mathdoc.fr/item/FAA_1986_20_4_a1/ %G ru %F FAA_1986_20_4_a1
M. L. Byalyi; L. V. Polterovich. Geodesic flows on the two-dimensional torus and phase transitions ``commensurability-noncommensurability''. Funkcionalʹnyj analiz i ego priloženiâ, Tome 20 (1986) no. 4, pp. 9-16. http://geodesic.mathdoc.fr/item/FAA_1986_20_4_a1/
[1] Aubry S., “The twist map, the extended Frenkel–Kontorova model and the devil's staircase”, Physica 7D, 1983, 240–258 | MR | Zbl
[2] Aubry S., Le Dceron P.Y., “The discrete Frenkel–Kontorova model and its extensions”, Physica, 8D, 1983, 381–422 | MR
[3] Herman M., “Sur les courbes invariantes par les diffeomorphismes de l'anneau”, Asterisque, 103–104 (1983), 3–38 | MR
[4] Morse H.M., “A fundamental class of geodesies on any closed surface of genus greater than one”, Trans. Amer. Math. Soc., 26, no. 1, 1924, 25–60 | DOI | MR | Zbl
[5] Hedlund G., “Geodesies on a two-dimensional Riemannian manifold with periodic coefficients”, Ann. of Math. Ser. 2, 33:4 (1932), 719–739 | DOI | MR
[6] Arnold V.I., Matematicheskie metody klassicheskoi mekhaniki, Nauka, M., 1979 | MR
[7] Kozlov V.V., “Variatsionnoe ischislenie i klassicheskaya mekhanika”, UMN, 40:2 (1985), 33–60 | MR | Zbl
[8] Alekseev V.M., Tikhomirov V.M., Fomin S.V., Optimalnoe upravlenie, Nauka, M., 1979 | MR
[9] Andronov A.A., Leontovich E.A., Gordon I.I., Maier A.G., Kachestvennaya teoriya dinamicheskikh sistem vtorogo poryadka, Nauka, M., 1966 | MR | Zbl
[10] Arnold V.I., Dopolnitelnye glavy teorii obyknovennykh differentsialnykh uravnenii, Nauka, M., 1978 | MR