메뉴 건너뛰기




Volumn 46, Issue 4, 1991, Pages 47-106

Statistical properties of two-dimensional hyperbolic billiards

Author keywords

[No Author keywords available]

Indexed keywords


EID: 84956084246     PISSN: 00360279     EISSN: None     Source Type: Journal    
DOI: 10.1070/RM1991v046n04ABEH002827     Document Type: Article
Times cited : (203)

References (47)
  • 1
    • 0002564801 scopus 로고
    • Geodesic flows on closed Riemannian manifolds of negative curvature
    • MR 36 # 7157
    • D.V. Anosov, Geodesic flows on closed Riemannian manifolds of negative curvature, Trudy Mat. Inst. Steklov. 90 (1967). MR 36 # 7157.
    • (1967) Trudy. Mat. Inst. Steklov , pp. 90
    • Anosov, D.V.1
  • 3
    • 0002336855 scopus 로고
    • Some smooth ergodic systems
    • MR 37 # 370
    • D.V. Anosov, and Ya. G. Sinai, Some smooth ergodic systems, Uspekhi Mat. Nauk 22:5 (1967), 107-172. MR 37 # 370.
    • (1967) Uspekhi Mat. Nauk , vol.22 , Issue.5 , pp. 107-172
    • Anosov, D.V.1    Sinai, Y.G.2
  • 6
    • 84956199963 scopus 로고
    • (Methods of symbolic dynamics: Collection of articles), Mir, Moscow
    • R. Bowen, Metódy simbolicheskoi dinamiki: Sb. statei (Methods of symbolic dynamics: Collection of articles), Mir, Moscow 1979.
    • (1979) Metódy Simbolicheskoi Dinamiki: Sb. Statei
    • Bowen, R.1
  • 7
    • 0000182012 scopus 로고
    • The fundamental theorem of the theory of scattering billiards
    • L.A. Bunimovich and Ya. G. Sinai, The fundamental theorem of the theory of scattering billiards, Mat. Sb. 90 (1973), 415-431. MR 51 # 3395.
    • (1973) Mat. Sb , vol.90 , pp. 415-431
    • Bunimovich, L.A.1    Sinai, Y.G.2
  • 9
    • 0003017867 scopus 로고
    • On billiards close to dispersing
    • D.V. Anosov, On billiards close to dispersing, Mat. Sb. 95 (1974), 49-73. MR 49 # 7422.
    • (1974) Mat. Sb. , vol.95 , pp. 49-73
    • Anosov, D.V.1
  • 11
    • 0000563360 scopus 로고
    • Decay of correlations in dynamical systems with chaotic behaviour
    • D.V. Anosov, Decay of correlations in dynamical systems with chaotic behaviour, Zh. Eksper. Teoret. Fiz. 89 (1985), 1452-1470.
    • (1985) Zh. Eksper. Teoret. Fiz , vol.89 , pp. 1452-1470
    • Anosov, D.V.1
  • 13
    • 0039264943 scopus 로고
    • Markov partitions for two-dimensional billiards, Uspekhi Mat
    • D.V. Anosov, Ya. G. Sinai, and N.I. Chernov, Markov partitions for two-dimensional billiards, Uspekhi Mat. Nauk 45:3 (1990), 97-134.
    • (1990) Nauk , vol.45 , Issue.3 , pp. 97-134
    • Anosov, D.V.1    Sinai, Y.G.2    Chernov, N.I.3
  • 15
    • 0039378715 scopus 로고
    • MR 34 # 2049, Translation: Independent and stationary sequences of random variables, Wolters- Noordhoflf, Groningen 1971
    • I.A. Ibragimov and Yu.V. Linnik, Nezavisimye i statsionamo svyazannye velichiny, Nauka, Moscow 1965. MR 34 # 2049. Translation: Independent and stationary sequences of random variables, Wolters- Noordhoflf, Groningen 1971.
    • (1965) Nezavisimye I Statsionamo Svyazannye Velichiny, Nauka, Moscow
    • Ibragimov, I.A.1    Linnik, Y.2
  • 16
    • 84956199964 scopus 로고
    • Moscow, MR 83a:28017. Translation: Ergodic theory, Springer-Verlag, New York 1982
    • I.P. Kornfel’d, Ya.G. Sinai, and S.V. Fomin, Ergodicheskaya teória, Nauka, Moscow 1980. MR 83a:28017. Translation: Ergodic theory, Springer-Verlag, New York 1982.
    • (1980) Ergodicheskaya teória, Nauka
    • Kornfel’D, I.P.1    Sinai, Y.2    Fomin, S.V.3
  • 19
    • 0002131294 scopus 로고
    • Markov partitions and Y-diffeomorphisms, Funktsional
    • MR 38 # 1361
    • Ya. G. Sinai, Markov partitions and Y-diffeomorphisms, Funktsional. Anal, i Prilozhen. 2:1 (1968), 64-89. MR 38 # 1361.
    • (1968) Anal, I Prilozhen , vol.2 , Issue.1 , pp. 64-89
    • Sinai, Y.G.1
  • 21
    • 0001379329 scopus 로고
    • Dynamical systems with elastic reflections. Ergodic properties of scattering billiards
    • D.V. Anosov, Dynamical systems with elastic reflections. Ergodic properties of scattering billiards, Uspekhi Mat. Nauk 25:2 (1970), 141-192. MR 43 # 481.
    • (1970) Uspekhi Mat. Nauk , vol.25 , Issue.2 , pp. 141-192
    • Anosov, D.V.1
  • 23
    • 84956071330 scopus 로고
    • Gibbs measures in ergodic theory
    • D.V. Anosov, Gibbs measures in ergodic theory, Uspekhi Mat. Nauk 27:4 (1972), 21-64. MR 53 # 3265.
    • (1972) Uspekhi Mat. Nauk , vol.27 , Issue.4 , pp. 21-64
    • Anosov, D.V.1
  • 25
    • 0009281855 scopus 로고
    • Ergodic properties of certain systems of two-dimensional discs and three-dimensional balls
    • D.V. Anosov, and N.I. Chernov, Ergodic properties of certain systems of two-dimensional discs and three-dimensional balls, Uspekhi Mat. Nauk. 42:3 (1987), 153-174. MR 89c: 58097.
    • (1987) Uspekhi Mat. Nauk , vol.42 , Issue.3 , pp. 153-174
    • Anosov, D.V.1    Chernov, N.I.2
  • 27
    • 84956199965 scopus 로고
    • (Current problems in mathematics, Fundamental directions, VINITI, Moscow, Translation: Dynamical systems II, Springer, Heidelberg
    • Sovremennye problémy matematiky. Fundamental’nye napravleniya (Current problems in mathematics: Fundamental directions), Vol. 2, VINITI, Moscow 1985. Translation: Dynamical systems II, Springer, Heidelberg 1989.
    • (1985) Fundamental’nye Napravleniya , vol.2
  • 28
    • 0010107975 scopus 로고
    • Topological entropy and periodic points of two-dimensional hyperbolic billiards
    • N.I. Chernov, Topological entropy and periodic points of two-dimensional hyperbolic billiards, Funktsional. Anal, i Prilozhen. 25:1 (1991), 50-57.
    • (1991) Funktsional. Anal, I Prilozhen , vol.25 , Issue.1 , pp. 50-57
    • Chernov, N.I.1
  • 29
    • 0002673989 scopus 로고
    • Numerical study of a d-dimensional periodic Lorentz gas with universal properties
    • J.-P. Bouchaud and P. Le Doussal, Numerical study of a d-dimensional periodic Lorentz gas with universal properties, J. Statist. Phys. 41:1-2 (1985), 225-248. MR 86k:82004.
    • (1985) J. Statist. Phys. , vol.41 , Issue.1-2 , pp. 225-248
    • Bouchaud, J.-P.1    Le Doussal, P.2
  • 30
    • 0003208028 scopus 로고
    • Equilibrium states and the ergodic theory of Anosov diffeomorphisms
    • R. Bowen, Equilibrium states and the ergodic theory of Anosov diffeomorphisms, Lecture Notes in Math. 470 (1975). MR 56 # 1364.
    • (1975) Lecture Notes in Math , vol.470
    • Bowen, R.1
  • 31
    • 0013501719 scopus 로고
    • The ergodic theory of axiom A flows
    • D.V. Anosov, and D. Ruelle, The ergodic theory of axiom A flows, Invent. Math. 29 (1975), 181-202. MR 52 # 1786.
    • (1975) Invent. Math , vol.29 , pp. 181-202
    • Anosov, D.V.1    Ruelle, D.2
  • 32
    • 29444443343 scopus 로고
    • On the ergodic properties of nowhere dispersing billiards
    • L.A. Bunimovich, On the ergodic properties of nowhere dispersing billiards, Comm. Math. Phys. 65 (1979), 295-312. MR 80h:58037.
    • (1979) Comm. Math. Phys. , vol.65 , pp. 295-312
    • Bunimovich, L.A.1
  • 33
    • 0000915121 scopus 로고
    • Markov partitions for dispersed billiards
    • D.V. Anosov, and Ya. G. Sinai, Markov partitions for dispersed billiards, Comm. Math. Phys. 77 (1980), 247-280. MR 82e:58059.
    • (1980) Comm. Math. Phys. , vol.77 , pp. 247-280
    • Anosov, D.V.1    Sinai, Y.G.2
  • 34
    • 11744373241 scopus 로고
    • Statistical properties of Lorentz gas with periodic configuration of scatters
    • D.V. Anosov, and Ya.G. Sinai, Statistical properties of Lorentz gas with periodic configuration of scatters, Comm. Math. Phys. 78 (1981), 479-497. MR 82m:82007.
    • (1981) Comm. Math. Phys. , vol.78 , pp. 479-497
    • Anosov, D.V.1    Sinai, Y.2
  • 35
    • 5544286933 scopus 로고
    • Markov partitions for dispersed billiards (Erratum)
    • D.V. Anosov, and Ya. G. Sinai, Markov partitions for dispersed billiards (Erratum), Comm. Math. Phys. 107 (1986), 357-358. MR 87m:58090.
    • (1986) Comm. Math. Phys. , vol.107 , pp. 357-358
    • Anosov, D.V.1    Sinai, Y.G.2
  • 36
    • 0000674670 scopus 로고
    • A theorem on ergodicity of two-dimensional hyperbolic billiards, Comm
    • D.V. Anosov, A theorem on ergodicity of two-dimensional hyperbolic billiards, Comm. Math. Phys. 130 (1990), 599-621.
    • (1990) Math. Phys , vol.130 , pp. 599-621
    • Anosov, D.V.1
  • 37
    • 0040130853 scopus 로고
    • Decay of correlations in certain hyperbolic systems
    • G. Casati, G. Comparin, and I. Guameri, Decay of correlations in certain hyperbolic systems, Phys. Rev. A26 (1982), 717-719.
    • (1982) Phys. Rev , vol.A26 , pp. 717-719
    • Casati, G.1    Comparin, G.2    Guameri, I.3
  • 38
    • 0001822139 scopus 로고
    • Billiards and Bernoulli schemes
    • G. Gallavotti and D. Omstein, Billiards and Bernoulli schemes, Comm. Math. Phys. 38 (1974), 83-101. MR 50 # 7480.
    • (1974) Comm. Math. Phys. , vol.38 , pp. 83-101
    • Gallavotti, G.1    Omstein, D.2
  • 39
    • 0002514975 scopus 로고
    • Théorèmes limites pour une classe de chaînes de Markovet applications aux difféomorphismes d’Anosov
    • Y. Guivarc’h and J. Hardy, Théorèmes limites pour une classe de chaînes de Markov et applications aux difféomorphismes d’Anosov, Ann. Inst. H. Poincaré. Probab. Statist. 24:1 (1988), 73-98. MR 89m:60080.
    • (1988) Ann. Inst. H. Poincaré. Probab. Statist. , vol.24 , Issue.1 , pp. 73-98
    • Guivarc’H, Y.1    Hardy, J.2
  • 40
    • 0003280184 scopus 로고
    • Smooth maps with singularities: Invariant manifolds, entropy and billiards
    • A. Katok and J.M. Strelcyn, Smooth maps with singularities: invariant manifolds, entropy and billiards, Lecture Notes in Math. 1222 (1987).
    • (1987) Lecture Notes in Math , pp. 1222
    • Katok, A.1    Strelcyn, J.M.2
  • 41
    • 0002090271 scopus 로고
    • The problem of recurrence for Lorentz processes
    • A. Krámli and D. Szász, The problem of recurrence for Lorentz processes, Comm. Math. Phys. 98 (1985), 539-552. MR 86m:60063.
    • (1985) Comm. Math. Phys , vol.98 , pp. 539-552
    • Krámli, A.1    Szász, D.2
  • 42
    • 0000059523 scopus 로고
    • A “transversal” fundamental theorem for semi-dispersing billiards, Comm
    • D.V. Anosov, N. Simànyi, and D. Szász, A “transversal” fundamental theorem for semi-dispersing billiards, Comm. Math. Phys. 129 (1990), 535-560.
    • (1990) Math. Phys , vol.129 , pp. 535-560
    • Anosov, D.V.1    Simànyi, N.2    Szász, D.3
  • 43
    • 0000591151 scopus 로고
    • Power law decay of correlations in a billiard problem
    • J. Machta, Power law decay of correlations in a billiard problem, J. Statist. Phys. 32 (1983), 555-564. MR 85e:70010.
    • (1983) J. Statist. Phys , vol.32 , pp. 555-564
    • Machta, J.1
  • 46
    • 84968514104 scopus 로고
    • Differentiable dynamical systems
    • D. Smale, Differentiable dynamical systems, Bull. Amer. Math. Soc. 73 (1967), 747-817. MR 37 # 3598. (Erratum: MR 39, p. 1593.)
    • (1967) Bull. Amer.Math. Soc. , vol.73 , pp. 747-817
    • Smale, D.1
  • 47
    • 0000441757 scopus 로고
    • Origin of long-time tails in strongly chaotic systems
    • F. Vivaldi, G Casati, and I. Guameri, Origin of long-time tails in strongly chaotic systems, Phys. Review Lett. 51 (1983), 727-730. MR 84k:58157.
    • (1983) Phys. Review Lett. , vol.51 , pp. 727-730
    • Vivaldi, F.1    Casati, G.2    Guameri, I.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.