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Mat. Sb. (N.S.), 1973, Volume 90(132), Number 3, Pages 415–431 (Mi msb3057)  

This article is cited in 31 scientific papers (total in 33 papers)

On a fundamental theorem in the theory of dispersing billiards

L. A. Bunimovich, Ya. G. Sinai

Abstract: 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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English version:
Mathematics of the USSR-Sbornik, 1973, 19:3, 407–423

Bibliographic databases:

UDC: 519.25
MSC: 28A65
Received: 02.02.1972

Citation: L. A. Bunimovich, Ya. G. Sinai, “On a fundamental theorem in the theory of dispersing billiards”, Mat. Sb. (N.S.), 90(132):3 (1973), 415–431; Math. USSR-Sb., 19:3 (1973), 407–423

Citation in format AMSBIB
\by L.~A.~Bunimovich, Ya.~G.~Sinai
\paper On~a~fundamental theorem in the theory of dispersing billiards
\jour Mat. Sb. (N.S.)
\yr 1973
\vol 90(132)
\issue 3
\pages 415--431
\jour Math. USSR-Sb.
\yr 1973
\vol 19
\issue 3
\pages 407--423

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    This publication is cited in the following articles:
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    19. L. A. Bunimovich, Ya. G. Sinai, N. I. Chernov, “Statistical properties of two-dimensional hyperbolic billiards”, Russian Math. Surveys, 46:4 (1991), 47–106  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    20. N. I. Chernov, S. Troubetzkoy, “Measures with infinite Lyapunov exponents for the periodic Lorentz gas”, J Statist Phys, 83:1-2 (1996), 193  crossref  mathscinet  zmath  adsnasa
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    24. G. M. Zaslavsky, M. Edelman, “Maxwell’s demon as a dynamical model”, Phys Rev E, 56:5 (1997), 5310  crossref  mathscinet  adsnasa  isi
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    26. L. A. Bunimovich, “Rasseyanie, defokusirovka i astigmatizm”, Matem. prosv., ser. 3, 5, MTsNMO, M., 2001, 106–124  mathnet
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    29. G. M. Zaslavsky, “Polynomial dispersion of trajectories in sticky dynamics”, Phys Rev E, 72:3 (2005), 036204  crossref  mathscinet  adsnasa  isi
    30. N. Chernov, “Advanced Statistical Properties of Dispersing Billiards”, J Statist Phys, 122:6 (2006), 1061  crossref  mathscinet  zmath  adsnasa  isi
    31. L. A. Bunimovich, “Criterion of absolute focusing for focusing component of billiards”, Reg Chaot Dyn, 14:1 (2009), 42  crossref  mathscinet  zmath  isi
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  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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