Geodesic
On a fundamental theorem in the theory of dispersing billiards
Sbornik. Mathematics, Tome 19 (1973) no. 3, pp. 407-423 Cet article a éte moissonné depuis la source Math-Net.Ru

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Billiards are considered within domains in the plane or on the two-dimensional torus with the euclidian metric, where the boundaries of these domains are everywhere convex inward. It is shown that the flow $\{S_t\}$ generated by such a billiard is a $K$-system. A fundamental place is here assigned to the proof of the theorem showing that transversal fibers for the flow $\{S_t\}$ consist “on the whole” of sufficiently long regular segments. From this theorem follow assertions on the absolute continuity of transversal fibers for the billiards in question. Figures: 8. Bibliography: 6 titles. 
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L. A. Bunimovich; Ya. G. Sinai. On a fundamental theorem in the theory of dispersing billiards. Sbornik. Mathematics, Tome 19 (1973) no. 3, pp. 407-423. http://geodesic.mathdoc.fr/item/SM_1973_19_3_a3/

[1] Ya. G. Sinai, “Dinamicheskie sistemy s uprugimi otrazheniyami”, Uspekhi matem. nauk, XXV:2 (152) (1970), 141–192 | MR

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

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[5] V. A. Rokhlin, “Izbrannye voprosy metricheskoi teorii dinamicheskikh sistem”, Uspekhi matem. nauk, IV:2 (30) (1949), 57–126

[6] E. Khopf, “Statistika geodezicheskikh linii na mnogoobraziyakh otritsatelnoi krivizny”, Uspekhi matem. nauk, IV:2 (30) (1949), 129–170