-
1
-
-
53949097517
-
-
P. Bachurin, P. Bálint and I. P. Tóth, Local ergodicity for systems with growth properties including multi-dimensional dispersing billiards, preprint, to appear in Israel Journal of Mathematics, 2007.
-
(2007)
Local ergodicity for systems with growth properties including multi-dimensional dispersing billiards, preprint, to appear in Israel Journal of Mathematics
-
-
Bachurin, P.1
Bálint, P.2
Tóth, I.P.3
-
2
-
-
53949096453
-
-
P. Batchourine, On the structure of singularity submanifolds of dispersing billiards, preprint, arXiv:0505620
-
P. Batchourine, On the structure of singularity submanifolds of dispersing billiards, preprint, arXiv:0505620
-
-
-
-
4
-
-
0031549891
-
Nowhere dispersing 3D billiards with non-vanishing Lyapunov exponents
-
L. A. Bunimovich and J. Rehacek, Nowhere dispersing 3D billiards with non-vanishing Lyapunov exponents, Commun. Math. Phys., 189 (1997), 729-757.
-
(1997)
Commun. Math. Phys
, vol.189
, pp. 729-757
-
-
Bunimovich, L.A.1
Rehacek, J.2
-
6
-
-
0036435079
-
Multi-dimensional semi-dispersing billiards: Singularities and the fundamental theorem
-
P. Bálint, N. Chernov, D. Szász and I. P. Tóth, Multi-dimensional semi-dispersing billiards: singularities and the fundamental theorem, Annales Henri Poincaré, 3 (2002), 451-482.
-
(2002)
Annales Henri Poincaré
, vol.3
, pp. 451-482
-
-
Bálint, P.1
Chernov, N.2
Szász, D.3
Tóth, I.P.4
-
7
-
-
0000182012
-
The fundamental theorem of the theory of scattering billiards
-
A. Bunimovich and Ya. G. Sinai, The fundamental theorem of the theory of scattering billiards, Mat. Sbornik, 90 (1973), 415-431.
-
(1973)
Mat. Sbornik
, vol.90
, pp. 415-431
-
-
Bunimovich, A.1
Sinai, Y.G.2
-
8
-
-
0012097571
-
A universal instability of many-dimensional oscillator systems
-
B. V. Chirikov, A universal instability of many-dimensional oscillator systems, Phys. Rep., 52 (1979), 263-379.
-
(1979)
Phys. Rep
, vol.52
, pp. 263-379
-
-
Chirikov, B.V.1
-
9
-
-
84878057601
-
Hyperbolic billiards and statistical physics
-
N. Chernov and D. Dolgopyat, Hyperbolic billiards and statistical physics, Proceedings ICM-2006, II. (2006), 1679-1704.
-
(2006)
Proceedings ICM-2006
, vol.2
, pp. 1679-1704
-
-
Chernov, N.1
Dolgopyat, D.2
-
10
-
-
34547280408
-
Flow-invariant hypersurfaces in semi-dispersing billiards
-
N. Chernov and N. Simányi, Flow-invariant hypersurfaces in semi-dispersing billiards, Annales Henri Poincaré, 8 (2007), 475-483.
-
(2007)
Annales Henri Poincaré
, vol.8
, pp. 475-483
-
-
Chernov, N.1
Simányi, N.2
-
12
-
-
0003280184
-
Invariant Manifolds, Entropy and Billiards; Smooth Maps with Singularities
-
A. Katok and J.-M. Strelcyn, "Invariant Manifolds, Entropy and Billiards; Smooth Maps with Singularities," Lecture Notes in Mathematics, 1222, 1986.
-
(1986)
Lecture Notes in Mathematics
, vol.1222
-
-
Katok, A.1
Strelcyn, J.-M.2
-
13
-
-
0000059523
-
A "transversal" fundamental theorem for semi-dispersing billiards
-
A. Krámli, N. Simányi and D. Szasz, A "transversal" fundamental theorem for semi-dispersing billiards, Commun. Math. Phys., 129 (1990), 535-560.
-
(1990)
Commun. Math. Phys
, vol.129
, pp. 535-560
-
-
Krámli, A.1
Simányi, N.2
Szasz, D.3
-
14
-
-
33751054663
-
-
Springer, Berlin
-
C. Liverani, Interacting particles, Encyclopaedia of Mathematical Sciences, Springer, Berlin, 101 (2000), 179-216.
-
(2000)
Interacting particles, Encyclopaedia of Mathematical Sciences
, vol.101
, pp. 179-216
-
-
Liverani, C.1
-
15
-
-
84961291543
-
Characteristic exponents and smooth ergodic theory
-
Ya. G. Pesin, Characteristic exponents and smooth ergodic theory, Russian Math. Surveys, 32 (1977), 55-112.
-
(1977)
Russian Math. Surveys
, vol.32
, pp. 55-112
-
-
Pesin, Y.G.1
-
16
-
-
84971972535
-
Dynamical systems with generalized hyperbolic attractors: Hyperbolic, ergodic and topological properties
-
Ya. G. Pesin, Dynamical systems with generalized hyperbolic attractors: hyperbolic, ergodic and topological properties, Ergodic Th. & Dynam. Sys., 12 (1992), 123-151.
-
(1992)
Ergodic Th. & Dynam. Sys
, vol.12
, pp. 123-151
-
-
Pesin, Y.G.1
-
17
-
-
0001200214
-
On the foundation of the ergodic hypothesis for a dynamical system of statistical mechanics
-
Ya. G. Sinai, On the foundation of the ergodic hypothesis for a dynamical system of statistical mechanics, Soviet Math. Dokl., 4 (1963), 1818-1822.
-
(1963)
Soviet Math. Dokl
, vol.4
, pp. 1818-1822
-
-
Sinai, Y.G.1
-
19
-
-
0000616278
-
The K-property of N billiard balls
-
II
-
N. Simányi, The K-property of N billiard balls, Invent. Math., I. 108 (1992), 521-548, II.
-
(1992)
Invent. Math
, vol.1
, Issue.108
, pp. 521-548
-
-
Simányi, N.1
-
20
-
-
53949115848
-
-
110 (1992), 151-172 (1181821).
-
110 (1992), 151-172 (1181821).
-
-
-
-
21
-
-
29644433764
-
Hard ball systems and semi-dispersive billiards: Hyperbolicity and ergodicity
-
N. Simányi, Hard ball systems and semi-dispersive billiards: hyperbolicity and ergodicity, Encyclopaedia of Mathematical Sciences, 101 (2000), 51-88.
-
(2000)
Encyclopaedia of Mathematical Sciences
, vol.101
, pp. 51-88
-
-
Simányi, N.1
-
22
-
-
0035981913
-
The complete hyperbolicity of cylindric billiards
-
N. Simányi, The complete hyperbolicity of cylindric billiards, Ergodic Th. & Dynam. Sys., 22 (2002), 281-302.
-
(2002)
Ergodic Th. & Dynam. Sys
, vol.22
, pp. 281-302
-
-
Simányi, N.1
-
23
-
-
2442538136
-
Proof of the ergodic hypothesis for typical hard ball systems
-
N. Simányi, Proof of the ergodic hypothesis for typical hard ball systems, Annales H. Poincaré, 5 (2004), 203-233.
-
(2004)
Annales H. Poincaré
, vol.5
, pp. 203-233
-
-
Simányi, N.1
-
24
-
-
53949123703
-
-
N. Simányi, Conditional proof of the Boltzmann-Sinai ergodic hypothesis, (Assuming the hyperbolicity of typical singular orbits.), 2007. arXiv:0605358
-
N. Simányi, Conditional proof of the Boltzmann-Sinai ergodic hypothesis, (Assuming the hyperbolicity of typical singular orbits.), 2007. arXiv:0605358
-
-
-
-
26
-
-
0009281855
-
Ergodic properties of some systems of two-dimensional disks and three-dimensional balls
-
Ya. G. Sinai and N. I. Chernov, Ergodic properties of some systems of two-dimensional disks and three-dimensional balls, Usp. Mat. Nauk, 42 (1987), 153-174.
-
(1987)
Usp. Mat. Nauk
, vol.42
, pp. 153-174
-
-
Sinai, Y.G.1
Chernov, N.I.2
-
27
-
-
0033241652
-
Hard ball systems are completely hyperbolic
-
N. Simányi and D. Szász, Hard ball systems are completely hyperbolic, Annals of Mathematics, 149 (1999), 35-96.
-
(1999)
Annals of Mathematics
, vol.149
, pp. 35-96
-
-
Simányi, N.1
Szász, D.2
-
28
-
-
0034421404
-
Non-integrability of cylindric billiards and transitive Lie-group actions
-
N. Simányi and D. Szász, Non-integrability of cylindric billiards and transitive Lie-group actions, Ergodic Th. & Dynam. Sys., 20 (2000), 593-610.
-
(2000)
Ergodic Th. & Dynam. Sys
, vol.20
, pp. 593-610
-
-
Simányi, N.1
Szász, D.2
-
29
-
-
0002298909
-
Ergodicity of classical billiard balls
-
D. Szász, Ergodicity of classical billiard balls, Physica A., 194 (1993), 86-92.
-
(1993)
Physica A
, vol.194
, pp. 86-92
-
-
Szász, D.1
-
30
-
-
1542574947
-
-
D. Szász, Boltzmann's ergodic hypothesis, a conjecture for centuries, Studia Sci. Math. Hung., 31 (1996), 299-322. (Reprinted in [30], 423-446).
-
D. Szász, Boltzmann's ergodic hypothesis, a conjecture for centuries, Studia Sci. Math. Hung., 31 (1996), 299-322. (Reprinted in [30], 423-446).
-
-
-
-
32
-
-
0032348050
-
Statistical properties of dynamical systems with some hyperbolicity
-
Lai-Sang Young, Statistical properties of dynamical systems with some hyperbolicity, Ann. of Math., 147 (1998), 585-650.
-
(1998)
Ann. of Math
, vol.147
, pp. 585-650
-
-
Young, L.-S.1
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