logo AFST
Non-uniformly hyperbolic billiards
Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 3 (1994) no. 2, pp. 223-257.
@article{AFST_1994_6_3_2_223_0,
     author = {Roberto Markarian},
     title = {Non-uniformly hyperbolic billiards},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     pages = {223--257},
     publisher = {Universit\'e Paul Sabatier},
     address = {Toulouse},
     volume = {Ser. 6, 3},
     number = {2},
     year = {1994},
     doi = {10.5802/afst.779},
     zbl = {0809.58030},
     mrnumber = {1283207},
     language = {en},
     url = {https://afst.centre-mersenne.org/articles/10.5802/afst.779/}
}
TY  - JOUR
TI  - Non-uniformly hyperbolic billiards
JO  - Annales de la Faculté des sciences de Toulouse : Mathématiques
PY  - 1994
DA  - 1994///
SP  - 223
EP  - 257
VL  - Ser. 6, 3
IS  - 2
PB  - Université Paul Sabatier
PP  - Toulouse
UR  - https://afst.centre-mersenne.org/articles/10.5802/afst.779/
UR  - https://zbmath.org/?q=an%3A0809.58030
UR  - https://www.ams.org/mathscinet-getitem?mr=1283207
UR  - https://doi.org/10.5802/afst.779
DO  - 10.5802/afst.779
LA  - en
ID  - AFST_1994_6_3_2_223_0
ER  - 
%0 Journal Article
%T Non-uniformly hyperbolic billiards
%J Annales de la Faculté des sciences de Toulouse : Mathématiques
%D 1994
%P 223-257
%V Ser. 6, 3
%N 2
%I Université Paul Sabatier
%C Toulouse
%U https://doi.org/10.5802/afst.779
%R 10.5802/afst.779
%G en
%F AFST_1994_6_3_2_223_0
Roberto Markarian. Non-uniformly hyperbolic billiards. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 3 (1994) no. 2, pp. 223-257. doi : 10.5802/afst.779. https://afst.centre-mersenne.org/articles/10.5802/afst.779/

[1] Arnold (V.I.) .- Mathematical Methods of Classifical Mechanics, New York - Heidelberg - Berlin, Springer 1978 (original Ed. 1974). | MR | Zbl

[2] Baldwin (P.R.) .- Soft Billiard Systems, Physica 29 D (1988), pp. 321-342. | MR | Zbl

[3] Bunimovich (L.A.) . - On billiards close to dispersing, Math USSR Sb. 23, n° 1 (1974), pp. 45-67. | MR | Zbl

[4] Bunimovich (L.A.) .- On ergodic properties of nowhere dispersing billiards, Commun. Math. Phys. 65 (1979), pp. 295-312. | MR | Zbl

[5] Bunimovich (L.A.) .- The Stochastic dynamics of rays on resonators, Izv. Vyssh. Uchebn. Zaved Radofiz 28 (1985), pp. 1601-1602 (in Russian). | MR

[6] Bunimovich (L.A.) .- Many dimensional nowhere dispersing billiards with chaotic behavior, Physica D 53 (1988), 58-64. | MR | Zbl

[7] Chernov (N.I.) . - Structure of transversal leaves in multidimensional semidispersing billiards, Funct. An. its Appl. 16, n° 1 (1982), pp. 270-280. | Zbl

[8] Cornfeld (I.P.), Fomin (S.V.) and Sinai (Ya.G.) .- Ergodic Theory, Berlin - Heidelberg - New York, Springer, 1982 (original Ed. 1980). | MR | Zbl

[9] Donnay (V.) .- Using Integrability to Produce Chaos: Billiards with Positive Entropy, Commun. Math. Phys. 141 (1991), pp. 225-257. | MR | Zbl

[10] Katok (A.) and Strelcyn (J.-M.) in collaboration with Ledrapier (F.) and Przytyki (F.) .- Smooth maps with singularities. Invariant Manifolds. Entropy and Billiards, Lecture Notes in Mathematics 1222, Berlin - Heidelberg - New York, Springer (1986). | MR | Zbl

[11] Kramli (A.), Simayi (N.) and Szász (D.) . - The K-Property of Three Billiard balls, Annals of Math. 133 (1991), pp. 37-72. | MR | Zbl

[12] Kubo (I.) .- Perturbed billiard Systems, I. The ergodicity of the motion of a particle in a compound central field, Nagoya Math. J. 61 (1976), pp. 1-57. | MR | Zbl

[13] Ledrappier (F.) and Young (L.S.) .- The metric entropy of diffeomorphisms, Part I, Annals of Math. 122 (1985), pp. 509-539. | MR | Zbl

[14] Lewowicz (J.) .- Lyapunov functions and topological stability, J. Differ. Equations 38 (1980), pp. 192-209. | MR | Zbl

[15] Lewowicz (J.) . - Lyapunov functions and stability of geodesic flows, In Lecture Notes in Mathematics 1007, Berlin - Heidelberg - New York, Springer (1981), pp. 463-479. | MR | Zbl

[16] Lewowicz (J.) .- Persistance in expansive systems, Ergodic Theory Dyn. Syst. 3 (1983), pp. 567-578. | MR | Zbl

[17] Lewowicz (J.) and Lima De Sa (E.) .- Analytical Models of pseudo Anosov maps, Ergodic Theory Dyn. Syst. 6 (1986), pp. 385-392. | MR | Zbl

[18] Markarian (R.) . - Billiards with Pesin region of Measure One, Commun. Math. Phys. 118 (1988), pp. 87-97. | MR | Zbl

[19] Pesin (Ya.B.) .- Familles of invariant manifolds corresponding to non zero. Characteristic exponents, Math. USSR Izvestija 10 (1976), pp. 1261-1305. | Zbl

[20] Pesin (Ya.B.) and Sinai (Ya.G.) .- Hyperbolicity and Stochasticity of Dynamical Systems, Soviet Scientific Reviews Section C, Mathematical Physics Review 4 (1981), pp. 53-115. | MR | Zbl

[21] Sinai (Ya.G.) .- On the foundations of the ergodic hypothesis for a dynamical system of Statistical Mechanics, Soviet Math. Dokl. 4 (1963), pp. 1818-1822. | MR

[22] Sinai (Ya.G.) .- Dynamical Systems with elastic reflections, Russian Math. Surv. 25, n° 1 (1970), pp. 137-189. | MR | Zbl

[23] Sinai (Ya.G.) .- Development of Krylov ideas. In Works on the foundations of Statistical Physics by N. S. Krylov, Princeton University 1979 (original Ed. 1977). | MR

[24] Sinai (Ya.G.) and Chernov (N.I.) .- Ergodic Properties of certain systems of two dimensional discs and three dimensional balls, Russ. Math. Surv. 42, n° 3 (1987), pp. 181-207. | MR | Zbl

[25] Wojtkowski (M.) .- Principles for the design of billiards with nonvanishing Lyapunov exponents, Commun. Math. Phys. 105 (1986), pp. 391-414. | MR | Zbl

Cited by Sources: