Geodesic
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 
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/
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[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