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@article{FAA_1991_25_3_a5,
author = {N. I. Chernov},
title = {New proof of {Sinai's} formula for the entropy of hyperbolic billiard systems. {Application} to {Lorentz} gases and {Bunimovich} stadiums},
journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
pages = {50--69},
publisher = {mathdoc},
volume = {25},
number = {3},
year = {1991},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/FAA_1991_25_3_a5/}
}
TY - JOUR AU - N. I. Chernov TI - New proof of Sinai's formula for the entropy of hyperbolic billiard systems. Application to Lorentz gases and Bunimovich stadiums JO - Funkcionalʹnyj analiz i ego priloženiâ PY - 1991 SP - 50 EP - 69 VL - 25 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/FAA_1991_25_3_a5/ LA - ru ID - FAA_1991_25_3_a5 ER -
%0 Journal Article %A N. I. Chernov %T New proof of Sinai's formula for the entropy of hyperbolic billiard systems. Application to Lorentz gases and Bunimovich stadiums %J Funkcionalʹnyj analiz i ego priloženiâ %D 1991 %P 50-69 %V 25 %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/item/FAA_1991_25_3_a5/ %G ru %F FAA_1991_25_3_a5
N. I. Chernov. New proof of Sinai's formula for the entropy of hyperbolic billiard systems. Application to Lorentz gases and Bunimovich stadiums. Funkcionalʹnyj analiz i ego priloženiâ, Tome 25 (1991) no. 3, pp. 50-69. http://geodesic.mathdoc.fr/item/FAA_1991_25_3_a5/
[1] Abramov L.M,, “Ob entropii potoka”, DAN SSSR, 128:5 (1959), 873–875 | MR | Zbl
[2] Bunimovich L.A., “O bilyardakh, blizkikh k rasseivayuschim”, Matem. sb., 94:1 (1974), 49–73 | MR | Zbl
[3] Bunimovich L.A., “Ob ubyvanii korrelyatsii v dinamicheskikh sistemakh s khaoticheskim povedeniem”, ZhETF, 89:4 (1985), 1452–1470
[4] Galperin G.A., “O sistemakh lokalno vzaimodeistvuyuschikh i ottalkivayuschikhsya chastits, dvizhuschikhsya v prostranstve”, Tr. MMO, 43, 1981, 142–196 | MR
[5] Elyutin P.V., “O kolmogorovskoi entropii billiarda ”, DAN SSSR, 291:3 (1986), 595–598 | MR
[6] Kolmogorov A.N., “Novyi metricheskii invariant tranzitivnykh dinamicheskikh sistem i endomorfizmov prostranstv Lebega”, DAN SSSR, 119:5 (1958), 861–864 | MR | Zbl
[7] Kornfeld I.P., Sinai Ya.G., Fomin S.V., Ergodicheskaya teoriya, Nauka, M., 1980 | MR
[8] Oseledets V.I., “Multiplikativnaya ergodicheskaya teorema. Kharakteristicheskie pokazateli Lyapunova dinamicheskikh sistem”, Tr. MMO, 19, 1968, 179–210 | Zbl
[9] Sinai Ya.G., “Dinamicheskie sistemy s uprugimi otrazheniyami. Ergodicheskie svoistva rasseivayuschikh bilyardov”, UMN, 25:2 (1970), 141–192 | MR | Zbl
[10] Sinai Ya.G., “Bilyardnye traektorii v mnogogrannom ugle”, UMN, 33:1 (1978), 229–230 | MR | Zbl
[11] Sinai Ya.G., “Ergodicheskie svoistva gaza Lorentsa”, Funktsion. analiz i ego pril., 13:3 (1979), 46–59 | MR | Zbl
[12] Sinai Ya.G., Chernov N.I., “Entropiya gaza tverdykh sfer po otnosheniyu k gruppe prostranstvenno-vremennykh sdvigov”, Tr. seminara im. I.G. Petrovskogo, no. 8, 1982, 218–238 | MR
[13] Sinai Ya.G., Chernov I.I., “Ergodicheskie svoistva nekotorykh sistem dvumernykh diskov i trekhmernykh sharov”, UMN, 42:3 (1987), 153–174 | MR | Zbl
[14] Sovremennye problemy matematiki. Fundamentalnye napravleniya, 2, VINITI, M., 1985
[15] Chernov N.I., “Postroenie transversalnykh sloev v mnogomernykh polurasseivayuschikh bilyardakh”, Funktsion. analiz i ego pril., 16:4 (1982), 35–46 | MR
[16] Benettin G., Strelcyn J.-M., “Numerical experiments on the free motion of a point massmoving in a plane convex region: Stochastic transition and entropy”, Phys. Rev. A, 17:2 (1978), 773–785 | DOI
[17] Bouchaud J.-P., Le Doussal P., “Numerical study of a c?-dimensional periodic Lorentz. gas with universal properties”, J. Stat. Phys., 41:1, 2 (1985), 225–248 | DOI | MR
[18] Bunimovich L.A., “On the ergodic properties of nowhere dispersing billiards”, Comm. Math. Phys., 65:3 (1979), 295–312 | DOI | MR | Zbl
[19] Federer H., “Curvature measures”, Trans. Amer. Math. Soc., 93, 1959, 418–491 | DOI | MR | Zbl
[20] Friedman V., OonoY., Kubo I., “Universal behaviour of Sinai billiard systems in thesmall-scatterer limit”, Phys. Rev. Lett., 52:9 (1984), 709–712 | DOI | MR
[21] Gallavotti G., Ornstein D., “Billiards and Bernoulli schemes”, Comm. Math. Phys., 38:2 (1974), 83–101 | DOI | MR | Zbl
[22] Illiner R., On the number of collisions in a hard sphere particle system in all space, Preprint, University of Victoria, Canada, 1988 | MR
[23] Katok A., Strelcyn J.-M., Smooth Maps v,ith Singularities: invariant manifolds, entropy and billiards, Lect. Notes Math., 1222, 1987 | MR
[24] Krómli A., Simónyi N., Szósz D., “Ergodic properties of semJdispersing billiards: 1. Two cylindric scatterers in the 3D torus”, Nonlinearity, 2:2 (1989), 311–326 | DOI | MR
[25] Krámli A., Simányi N., Szász D., “A 'transversal' fundamental theorem for semi-dispersing billiards”, Comm. Math. Phys., 129:3 (1990), 535–560 | DOI | MR | Zbl
[26] Krámli A., Simányi N., Szász D., “The $K$-property of three billiard balls”, Ann. of Math. (2), 133:1 (1991), 37–72 | DOI | MR | Zbl
[27] Kubo I., “Perturbed billiard systems I”, Nagoya Math. J., 61 (1976), 1–57 | DOI | MR | Zbl
[28] Markarian R., “Billiards with Pesin region of measure one”, Comm. Math. Phys., 118:1 (1988), 87–97 | DOI | MR | Zbl
[29] Sinai Ya.G., Entropy per particle for the dynamical system of hard spheres, Preprint, Harvard University, 1978
[30] Wojtkowski M., “Principles for the design of billiards with nonvanishing Lyapunov exponents”, Comm. Math. Phys., 105:3 (1986), 391–414 | DOI | MR | Zbl
[31] Woitkowski M., “Measure theoretic entropy of the system of hard spheres”, Ergod. Theory Dyn. Syst., 8:1 (1988), 133–153 | DOI | MR
[32] Zaslavsky G.M., “Stochasticity in Quantum Systems”, Phys. Rep., 80:3 (1981), 157–250 | DOI | MR