Geodesic
On billiards close to dispersing
Sbornik. Mathematics, Tome 23 (1974) no. 1, pp. 45-67 
L. A. Bunimovich. On billiards close to dispersing. Sbornik. Mathematics, Tome 23 (1974) no. 1, pp. 45-67. http://geodesic.mathdoc.fr/item/SM_1974_23_1_a2/
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Voir la notice de l'article provenant de la source Math-Net.Ru

One considers dynamical systems generated by billiards which are “perturbations” of dispersing billiards. It is shown that such dynamical systems are systems of A. N. Kolmogorov ($K$-systems), if the “perturbation” satisfies certain conditions which have an intuitive geometric interpretation. Bibliography: 12 titles.

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[2] V. A. Rokhlin, “Lektsii po entropiinoi teorii preobrazovanii s invariantnoi meroi”, Uspekhi matem. nauk, XXII:5 (137) (1967), 3–56

[3] L. A. Bunimovich, Ya. G. Sinai, “Ob osnovnoi teoreme teorii rasseivayuschikh bilyardov”, Matem. sb., 90 (132) (1973), 415–431 | Zbl

[4] V. I. Arnold, “Malye znamenateli i problema ustoichivosti dvizheniya v klassicheskoi i nebesnoi mekhanike”, Uspekhi matem. nauk, XVIII:6 (114) (1963), 91–192 | MR

[5] E. Hopf, “Statistic der Lösunger geodätisher Probleme von unstabilen Typus, II”, Math. Ann., 117:4 (1940), 590–608 | DOI | MR | Zbl

[6] D. V. Anosov, Ya. G. Sinai, “Nekotorye gladkie ergodicheskie sistemy”, Uspekhi matem. nauk, XXII:5 (137) (1967), 107–172 | MR

[7] V. A. Rokhlin, “Izbrannye voprosy metricheskoi teorii dinamicheskikh sistem”, Uspekhi matem. nauk, IV:2 (30) (1949), 57–128

[8] A. N. Khovanskii, Prilozhenie tsepnykh drobei i ikh obobschenii k voprosam priblizhennogo analiza, Gostekhizdat, Moskva, 1956

[9] A. Ya. Khinchin, Tsepnye drobi, Fizmatgiz, Moskva, 1961

[10] D. V. Anosov, “Geodezicheskie potoki na zamknutykh rimanovykh mnogoobraziyakh otritsatelnoi krivizny”, Trudy Matem. in-ta im. V. A. Steklova, XC (1967)

[11] Ya. G. Sinai, “Klassicheskie dinamicheskie sistemy so schetnokratnym lebegovskim spektrom”, Izv. AN SSSR, seriya matem., 30 (1966), 15–68 | MR | Zbl

[12] Dzh. D. Birkgof, Dinamicheskie sistemy, Gostekhizdat, Moskva, 1941