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Volumn 21, Issue 10, 2008, Pages

Some challenges in the theory of (semi)-dispersing billiards

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EID: 56349113851     PISSN: 09517715     EISSN: 13616544     Source Type: Journal    
DOI: 10.1088/0951-7715/21/10/T02     Document Type: Article
Times cited : (15)

References (33)
  • 1
    • 0002228008 scopus 로고
    • Remarks on quasi-crystalline symmetries
    • Arnold V I 1988 Remarks on quasi-crystalline symmetries Physica D 33 21-5
    • (1988) Physica , vol.33 , Issue.1-3 , pp. 21-25
    • Arnold, V.I.1
  • 3
    • 84956084246 scopus 로고
    • Statistical properties of two dimensional dispersing billiards
    • Bunimovich L A, Chernov N I and Sinai Ya G 1991 Statistical properties of two dimensional dispersing billiards Russ. Math. Surv. 46 47-106
    • (1991) Russ. Math. Surv. , vol.46 , Issue.4 , pp. 47-106
    • Bunimovich, L.A.1    Chernov, N.I.2    Sinai Ya, G.3
  • 4
    • 0036435079 scopus 로고    scopus 로고
    • Multi-dimensional semi-dispersing billiards: Singularities and the fundamental theorem
    • Bálint P, Chernov N, Szász D and Tóth I P 2002 Multi-dimensional semi-dispersing billiards: singularities and the fundamental theorem Ann. Henri Poincaré 3 451-82
    • (2002) Ann. Henri Poincaré , vol.3 , Issue.3 , pp. 451-482
    • Bálint, P.1    Chernov, N.2    Szász, D.3    Tóth, I.P.4
  • 5
    • 21244435939 scopus 로고    scopus 로고
    • Geometry of multi-dimensional dispersing billiards
    • Bálint P, Chernov N, Szász D and Tóth I P 2003 Geometry of multi-dimensional dispersing billiards Astérisque 286 119-50
    • (2003) Astérisque , vol.286 , pp. 119-150
    • Bálint, P.1    Chernov, N.2    Szász, D.3    Tóth, I.P.4
  • 6
    • 11744373241 scopus 로고
    • Statistical properties of Lorentz gas with periodic configuration of scatterers
    • Bunimovich L A and Sinai Ya G 1981 Statistical properties of Lorentz gas with periodic configuration of scatterers Commun. Math. Phys. 78 479-97
    • (1981) Commun. Math. Phys. , vol.78 , Issue.4 , pp. 479-497
    • Bunimovich, L.A.1    Sinai Ya, G.2
  • 7
    • 55549087864 scopus 로고    scopus 로고
    • Exponential decay of correlations in multi-dimensional dispersing billiards
    • Bálint P and Tóth I P 2008 Exponential decay of correlations in multi-dimensional dispersing billiards Ann. H Poincaré at press
    • (2008) Ann. H Poincaré
    • Bálint, P.1    Tóth, I.P.2
  • 8
    • 56349170376 scopus 로고    scopus 로고
    • Local ergodicity for systems with growth properties including multi-dimensional dispersing billiards
    • Bachurin P, Bálint P and Tóth I P 2008 Local ergodicity for systems with growth properties including multi-dimensional dispersing billiards Israel J. Math. at press
    • (2008) Israel J. Math.
    • Bachurin, P.1    Bálint, P.2    Tóth, I.P.3
  • 9
    • 0033074305 scopus 로고    scopus 로고
    • Decay of correlations and dispersing billiards
    • Chernov N I 1999 Decay of correlations and dispersing billiards J. Stat. Phys. 94 513-56
    • (1999) J. Stat. Phys. , vol.94 , pp. 513-556
    • Chernov, N.I.1
  • 11
    • 56349121705 scopus 로고    scopus 로고
    • Chernov N and Markarian R 2006 Chaotic Billiards (Mathematical Surveys and Monographs) vol 127 (Providence, RI: American Mathematical Society)
    • (2006) Chaotic Billiards , vol.127
    • Chernov, N.1    Markarian, R.2
  • 12
    • 0033481532 scopus 로고    scopus 로고
    • Parabolic Harnack inequality and estimates of Markov chains on graphs
    • Delmotte T 1999 Parabolic Harnack inequality and estimates of Markov chains on graphs Revista Matemaática Iberoamericana 1 1810-232
    • (1999) Revista Matemaática Iberoamericana , vol.1 , pp. 1810-1232
    • Delmotte, T.1
  • 13
    • 42549168128 scopus 로고    scopus 로고
    • Recurrence properties of planar Lorentz process
    • Dolgopyat D, Szász D and Varj T 2008 Recurrence properties of planar Lorentz process Duke Math. J. 142 241-81
    • (2008) Duke Math. J. , vol.142 , Issue.2 , pp. 241-281
    • Dolgopyat, D.1    Szász, D.2    Varj, T.3
  • 14
    • 56349137317 scopus 로고    scopus 로고
    • Limit theorems for locally perturbed Lorentz processes
    • Dolgopyat D, Szász D and Varj T 2008 Limit theorems for locally perturbed Lorentz processes Duke Math. J. http://www.math.bme.hu/∼szasz/
    • (2008) Duke Math. J.
    • Dolgopyat, D.1    Szász, D.2    Varj, T.3
  • 16
    • 33645925541 scopus 로고    scopus 로고
    • Heat kernel estimates for symmetric random walks on a class of fractal graphs and applications
    • Hambly B M and Kumagai T 2004 Heat kernel estimates for symmetric random walks on a class of fractal graphs and applications Proc. Symp. Pure Math. Part 2 72 233-59
    • (2004) Proc. Symp. Pure Math. , vol.72 , pp. 233-259
    • Hambly, B.M.1    Kumagai, T.2
  • 17
    • 0034502904 scopus 로고    scopus 로고
    • Random walks and localization on the Penrose lattice
    • Kunz M 2000 Random walks and localization on the Penrose lattice Physica B 293 164-82
    • (2000) Physica , vol.293 , Issue.1-2 , pp. 164-182
    • Kunz, M.1
  • 18
    • 0000593586 scopus 로고
    • Ergodic properties of semi-dispersing billiards: I. Two cylindric scatterers in the 3-D torus
    • Krámli A, Simányi N and Szász D 1989 Ergodic properties of semi-dispersing billiards: I. Two cylindric scatterers in the 3-D torus Nonlinearity 2 311-26
    • (1989) Nonlinearity , vol.2 , Issue.2 , pp. 311-326
    • Krámli, A.1    Simányi, N.2    Szász, D.3
  • 19
    • 0000059523 scopus 로고
    • A 'transversal' fundamental theorem for semi-dispersing billiards
    • Krámli A, Simányi N and Szász D 1990 A 'transversal' fundamental theorem for semi-dispersing billiards Commun. Math. Phys. 129 535-60
    • (1990) Commun. Math. Phys. , vol.129 , Issue.3 , pp. 535-560
    • Krámli, A.1    Simányi, N.2    Szász, D.3
  • 22
    • 0001200214 scopus 로고
    • On the foundation of the ergodic hypothesis for a dynamical system of statistical mechanics
    • Sinai Ya G 1963 On the foundation of the ergodic hypothesis for a dynamical system of statistical mechanics Sov. Math.-Dokl. 4 1818-22
    • (1963) Sov. Math.-Dokl. , vol.4 , pp. 1818-1822
    • Sinai Ya, G.1
  • 23
    • 84927896522 scopus 로고
    • Dynamical systems with elastic reflections: Ergodic properties of dispersing billiards
    • Sinai Ya G 1970 Dynamical systems with elastic reflections: ergodic properties of dispersing billiards Russ. Math. Surv. 25 137-89
    • (1970) Russ. Math. Surv. , vol.25 , Issue.2 , pp. 137-189
    • Sinai Ya, G.1
  • 25
    • 0009281855 scopus 로고
    • Ergodic properties of some systems of 2-D discs and 3-D spheres
    • Sinai Ya G and Chernov N I 1987 Ergodic properties of some systems of 2-D discs and 3-D spheres Usp. Mat. Nauk 42 153-74
    • (1987) Usp. Mat. Nauk , vol.42 , pp. 153-174
    • Sinai Ya, G.1    Chernov, N.I.2
  • 27
    • 0034421404 scopus 로고    scopus 로고
    • Non-integrability of cylindric billiards and transitive Lie-group actions
    • Simányi N and Szász D 2000 Non-integrability of cylindric billiards and transitive Lie-group actions Ergod. Theory Dyn. Syst. 20 593-610
    • (2000) Ergod. Theory Dyn. Syst. , vol.20 , Issue.2 , pp. 593-610
    • Simányi, N.1    Szász, D.2
  • 28
    • 0039879198 scopus 로고
    • Joint diffusion on the line
    • Szász D 1980 Joint diffusion on the line J. Stat. Phys. 23 231-40
    • (1980) J. Stat. Phys. , vol.23 , Issue.2 , pp. 231-240
    • Szász, D.1
  • 29
    • 0002298909 scopus 로고
    • Ergodicity of classical billiard balls
    • Szász D 1993 Ergodicity of classical billiard balls Physica A 194 86-92
    • (1993) Physica , vol.194 , Issue.1-4 , pp. 86-92
    • Szász, D.1
  • 30
  • 31
    • 53949103964 scopus 로고    scopus 로고
    • Algebro-geometric methods for hard ball systems
    • Szász D 2008 Algebro-geometric methods for hard ball systems Discrete Cont. Dyn. Syst. Ser. A 22 427-43
    • (2008) Discrete Cont. Dyn. Syst. , vol.22 , pp. 427-443
    • Szász, D.1
  • 32
    • 56349156213 scopus 로고    scopus 로고
    • Penrose tilings and noncommutative geometry
    • Tasnády T and Petz D 2008 Penrose tilings and noncommutative geometry WSPC Proc.
    • (2008) WSPC Proc.
    • Tasnády Petz T, D.1
  • 33
    • 0032348050 scopus 로고    scopus 로고
    • Statistical properties of dynamical systems with some hyperbolicity
    • Young L-S 1998 Statistical properties of dynamical systems with some hyperbolicity Ann. Math. 147 585-650
    • (1998) Ann. Math. , vol.147 , Issue.3 , pp. 585-650
    • Young, L.-S.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.