Geometry of multi-dimensional dispersing billiards

Bálint, Péter ; Chernov, Nikolai ; Szász, Domokos ; Tóth, Imre Péter

Geometric methods in dynamics (I) : Volume in honor of Jacob Palis, Astérisque, no. 286 (2003), pp. 119-150.

MR Zbl

@incollection{AST_2003__286__119_0,
     author = {B\'alint, P\'eter and Chernov, Nikolai and Sz\'asz, Domokos and T\'oth, Imre P\'eter},
     title = {Geometry of multi-dimensional dispersing billiards},
     booktitle = {Geometric methods in dynamics (I) : Volume in honor of Jacob Palis},
     editor = {de Melo, Wellington and Viana, Marcelo and Yoccoz, Jean-Christophe},
     series = {Ast\'erisque},
     pages = {119--150},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {286},
     year = {2003},
     mrnumber = {2052299},
     zbl = {1060.37030},
     language = {en},
     url = {http://www.numdam.org/item/AST_2003__286__119_0/}
}

TY  - CHAP
AU  - Bálint, Péter
AU  - Chernov, Nikolai
AU  - Szász, Domokos
AU  - Tóth, Imre Péter
TI  - Geometry of multi-dimensional dispersing billiards
BT  - Geometric methods in dynamics (I) : Volume in honor of Jacob Palis
AU  - Collectif
ED  - de Melo, Wellington
ED  - Viana, Marcelo
ED  - Yoccoz, Jean-Christophe
T3  - Astérisque
PY  - 2003
SP  - 119
EP  - 150
IS  - 286
PB  - Société mathématique de France
UR  - http://www.numdam.org/item/AST_2003__286__119_0/
LA  - en
ID  - AST_2003__286__119_0
ER  -

%0 Book Section
%A Bálint, Péter
%A Chernov, Nikolai
%A Szász, Domokos
%A Tóth, Imre Péter
%T Geometry of multi-dimensional dispersing billiards
%B Geometric methods in dynamics (I) : Volume in honor of Jacob Palis
%A Collectif
%E de Melo, Wellington
%E Viana, Marcelo
%E Yoccoz, Jean-Christophe
%S Astérisque
%D 2003
%P 119-150
%N 286
%I Société mathématique de France
%U http://www.numdam.org/item/AST_2003__286__119_0/
%G en
%F AST_2003__286__119_0

Bálint, Péter; Chernov, Nikolai; Szász, Domokos; Tóth, Imre Péter. Geometry of multi-dimensional dispersing billiards, dans Geometric methods in dynamics (I) : Volume in honor of Jacob Palis, Astérisque, no. 286 (2003), pp. 119-150. http://www.numdam.org/item/AST_2003__286__119_0/

Bibliographie
Cité par

[AGV]V. I. Arnold, S. M. Gusein-Zade, A. N. Varchenko; Singularities of differentiable maps I., Monographs in Mathematics 82, Birkhauser Boston, 1985 | MR | Zbl

[BChSzT] P. Bálint, N. I. Chernov, D. Szász and I. P. Tóth, Multi-dimensional Semi-dispersing Billiards : Singularities and the Fundamental Theorem, Ann. Henri Poincaré 3 (2002), 451-482. | DOI | MR | Zbl

[Bl] P. Bleher, Statistical properties of two-dimensional periodic Lorentz gas with infinite horizon, J. Statist, Phys. 66 (1992), 315-373. | DOI | MR | Zbl

[Bo] L. Boltzmann, Über die Eigenschaften monocyklischer und anderer damit verwandter Systeme, Kronecker J. = J. Reine Angew. Math. 98 (1884) 68-94, Jahrbuch Fortschritte Math. 16 863 | EuDML | JFM | MR

[BSC1] L. A. Bunimovich, Ya. G. Sinai and N. I. Chernov, Markov partitions for two-dimensional billiards, Russ. Math. Surv. 45 (1990), 105-152. | DOI | MR | Zbl

[BSC2] L. A. Bunimovich, Ya. G. Sinai and N. I. Chernov, Statistical properties of two-dimensional hyperbolic billiards, Russ. Math. Surv. 46 (1991), 47-106. | DOI | MR | Zbl

[BR] L. A. Bunimovich and J. Reháček, How high dimensional stadia look like, Commun. Math. Phys. 197 (1998) 277-301. | DOI | MR | Zbl

[CELS1] N. I. Chernov, G. L. Eyink, J. L. Lebowitz and Ya. G. Sinai, Steady-state electrical conduction in the periodic Lorentz gas, Comm. Math. Phys. 154 (1993), 569-601. | DOI | MR | Zbl

[CELS2] N. I. Chernov, G. L. Eyink, J. L. Lebowitz and Ya. G. Sinai, Derivation of Ohm's law in a deterministic mechanical model, Phys. Rev. Let. 70 (1993), 2209-2212. | DOI

[Ch1] N. Chernov, Statistical properties of the periodic Lorentz gas. Multidimensional case. J. Statist. Phys. 74 (1994), 11-53 | DOI | MR | Zbl

[Ch2] N. Chernov, Decay of correlations and dispersing billiards, J. Statist. Phys. 94 (1999), 513-556. | DOI | MR | Zbl

[Ch3] N. Chernov, Sinai billiards under small external forces, Ann. Henri Poincaré 2 (2001), 197-236. | DOI | MR | Zbl

[Co] J. P. Conze, Sur un critère de récurrence en dimension $2$ pour les marches stationnaires, applications, Ergod. Th. Dynam. Sys. 19 (1999), 1233-1245. | DOI | MR | Zbl

[DM] C. P. Dettmann and G. P. Morriss, Crisis in the periodic Lorentz gas, Phys. Rev. E. 54 (1996), 4782-4790. | DOI

[GO] G. Gallavotti and D. Ornstein, Billiards and Bernoulli schemes, Comm. Math. Phys. 38 (1974), 83-101. | DOI | MR | Zbl

[GC] G. Gallavotti and E. D. G. Cohen, Dynamical ensembles in stationary states, J. Stat. Phys. 80 (1995), 931-970. | DOI | MR | Zbl

[KSSz] A. Krámli, N. Simányi and D. Szász, A "Transversal" Fundamental Theorem for Semi-Dispersing Billiards, Comm. Math. Phys. 129 (1990), 535-560. | DOI | MR | Zbl

[KSz] A. Krámli and D. Szász, The problem of recurrence for the Lorentz process, Commun. Math. Phys. 98 (1985), 539-552. | DOI | MR | Zbl

[Ru] D. Ruelle, Smooth dynamics and new theoretical ideas in nonequilibrium statistical mechanics, J. Statist. Phys. 94 (1999). | MR | Zbl

[Schm] K. Schmidt, On joint recurrence, C.R. Acad. Sci. Paris Séc. I. Math. 327 (1998) 837-842. | DOI | MR | Zbl

[Si] Ya. G. Sinai, Dynamical systems with elastic reflections. Ergodic properties of dispersing billiards, Russ. Math. Surv. 25 (1970), 137-189. | DOI | MR | Zbl

[SCh] Ya. G. Sinai and N. Chernov, Ergodic Properties of Certain Systems of $2 - D$ Discs and $3 - D$ Balls., Russain Mathematical Surveys, (3) 42, 181-201, (1987). | DOI | MR

[Y1] L.-S. Young, Statistical properties of dynamical systems with some hyperbolicity, Annals of Math. 147 (1998), 585-650. | DOI | MR | Zbl

[Y2] L.-S. Young, Ergodic theory of chaotic dynamical systems, XIIth International Congress of Mathematical Physics (ICMP'97) (Brisbane), 131-143, Internat. Press, Cambridge, MA, 1999. | MR | Zbl