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Uspekhi Mat. Nauk, 1987, Volume 42, Issue 3(255), Pages 153–174 (Mi umn2540)  

This article is cited in 67 scientific papers (total in 69 papers)

Ergodic properties of certain systems of two-dimensional discs and three-dimensional balls

Ya. G. Sinai, N. I. Chernov


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English version:
Russian Mathematical Surveys, 1987, 42:3, 181–207

Bibliographic databases:

UDC: 517.53/.57
MSC: 37A25, 57R30, 37D50
Received: 01.06.1985
Revised: 23.02.1987

Citation: Ya. G. Sinai, N. I. Chernov, “Ergodic properties of certain systems of two-dimensional discs and three-dimensional balls”, Uspekhi Mat. Nauk, 42:3(255) (1987), 153–174; Russian Math. Surveys, 42:3 (1987), 181–207

Citation in format AMSBIB
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\by Ya.~G.~Sinai, N.~I.~Chernov
\paper Ergodic properties of certain systems of two-dimensional discs and three-dimensional balls
\jour Uspekhi Mat. Nauk
\yr 1987
\vol 42
\issue 3(255)
\pages 153--174
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\transl
\jour Russian Math. Surveys
\yr 1987
\vol 42
\issue 3
\pages 181--207
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    Citing articles on Google Scholar: Russian citations, English citations
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    1. L. A. Bunimovich, Ya. G. Sinai, N. I. Chernov, “Markov partitions for two-dimensional hyperbolic billiards”, Russian Math. Surveys, 45:3 (1990), 105–152  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. N. I. Chernov, “New proof of Sinai's formula for the entropy of hyperbolic billiard systems. Application to Lorentz gases and Bunimovich stadiums”, Funct. Anal. Appl., 25:3 (1991), 204–219  mathnet  crossref  mathscinet  zmath  isi
    3. 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
    4. N. I. Chernov, “Ergodicity of a Hamiltonian system of two particles in an exterior field”, Russian Math. Surveys, 46:5 (1991), 187–188  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    5. Pierre Gaspard, “Diffusion, effusion, and chaotic scattering: An exactly solvable Liouvillian dynamics”, J Statist Phys, 68:5-6 (1992), 673  crossref  mathscinet  zmath  isi
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    8. R Markarian, Nonlinearity, 6:5 (1993), 819  crossref  mathscinet  zmath  adsnasa  isi
    9. N. I. Chernov, “On Local Ergodicity in Hyperbolic Systems with Singularities”, Funct. Anal. Appl., 27:1 (1993), 51–54  mathnet  crossref  mathscinet  zmath  isi
    10. N. I. Chernov, “Statistical properties of the periodic Lorentz gas. Multidimensional case”, J Statist Phys, 74:1-2 (1994), 11  crossref  mathscinet  zmath  adsnasa  isi  elib
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    13. J. R. Dorfman, “Chaotic scattering theory of transport and reaction-rate coefficients”, Phys Rev E, 51:1 (1995), 28  crossref  mathscinet  adsnasa  isi
    14. P. Gaspard, “Chaotic scattering theory, thermodynamic formalism, and transport coefficients”, Phys Rev E, 52:4 (1995), 3525  crossref  mathscinet  adsnasa  isi
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    16. 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  isi
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    24. N Chernov, S Troubetzkoy, Nonlinearity, 11:4 (1998), 1095  crossref  mathscinet  zmath  adsnasa  isi
    25. Pierre Gaspard, “Microscopic chaos and chemical reactions”, Physica A: Statistical Mechanics and its Applications, 263:1-4 (1999), 315  crossref
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