Billards en polygones et groupes fuchsiens
Séminaire de théorie spectrale et géométrie, Tome 14 (1995-1996), pp. 109-120. 
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     title = {Billards en polygones et groupes fuchsiens},
     journal = {S\'eminaire de th\'eorie spectrale et g\'eom\'etrie},
     pages = {109--120},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {14},
     year = {1995-1996},
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     url = {http://archive.numdam.org/item/TSG_1995-1996__14__109_0/}
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Gutkin, Eugène. Billards en polygones et groupes fuchsiens. Séminaire de théorie spectrale et géométrie, Tome 14 (1995-1996), pp. 109-120. http://archive.numdam.org/item/TSG_1995-1996__14__109_0/

[1] P. Arnoux, Ergodicité générique des billards polygonaux, Séminaire Bourbaki, 696 ( 1988), 203-221. | Numdam | MR | Zbl

[2] P. Arnoux, Echanges d'intervalles et flots sur les surfaces, Enseignement Mathématique, Monographie 29 ( 1981), 5-38. | MR | Zbl

[3] A. Beardon, The Geometry of Discrete Groups, Springer-Verlag, New York, 1983. | MR | Zbl

[4] E. Gutkin, Billiard flows on almost integrable polyhedral surfaces, Ergod. Theor. & Dyn. Sys. 4 ( 1984), 569-584. | MR | Zbl

[5] E. Gutkin, Billiards in polygons, Physica 19 D ( 1986), 311-333. | MR | Zbl

[6] E. Gutkin, Billiards in polygons: survey of recent results, J. Stat. Phys. 83 ( 1996), 7-26. | MR | Zbl

[7] E. Gutkin and N. Haydn, Topological entropy of generalized polygon exchanges, Bull. AMS 32 ( 1995), 50-57. | MR | Zbl

[8] E. Gutkin and N. Haydn, Topological entropy of polygon exchange transformations and polygonal billiards, Ergod. Theor. & Dyn. Sys., sous presse. | Zbl

[9] E. Gutkin and C. Judge, The geometry and arithmetic of translation surfaces, with applications to polygonal billiards, Math. Res. Lett. 3 ( 1996), 391-03. | MR | Zbl

[10] E. Gutkin and C. Judge, Affine coverings of translation surfaces, billiards, and arithmetic lattices, prépublication, 1996.

[11] E. Gutkin and S. Troubetzkoy, Directional flows and strong recurrence for polygonal billiards, Pittman Res. Notes in Math., sous presse. | Zbl

[12] C. Judge, On the existence of Maas cusp forms on hyperbolic surfaces with cone points, Journal of the A.M.S. 8 ( 1995), 715-759. | MR | Zbl

[13] C. Judge, On the angular moduli of constant curvature surfaces with conic singularities, prépublication, 1995.

[14] A. Katok, The growth rate for the number of singular and periodic orbits for a polygonal billiard, Comm. Math. Phys. 111 ( 1987), 151-160. | MR | Zbl

[15] R. Kenyon and J. Smillie, Billiards in rational-angled triangles, prépublication, 1996. | Zbl

[16] S. Kerckhoff, H. Masur, and J. Smillie, Ergodicity of billiard flows and quadratic differentials, Ann. Math. 124 ( 1986), 293-311. | MR | Zbl

[17] H. Masur, Interval exchange transformations and measured foliations, Ann.Math. 115( 1982), 169-200. | MR | Zbl

[18] H. Masur, Lower bounds for the number of saddle connections, and closed trajectories of a quadralic differential, MSRI Publ. vol. 10 ( 1988), 215-228. | MR | Zbl

[19] H. Masur, The growth rate of trajectories of a quadratic differential, Ergod. Theor. & Dyn. Sys. 10 ( 1990), 151-176. | MR | Zbl

[20] S. Tabachnikov, Billiards, Panoramas et Synthèses, n.l, Soc. Math. France, 1995. | MR | Zbl

[21] W. Thurston, The Geometry and Topology of 3-Manifolds, Princeton Lecture Notes, 1978.

[22] W. A. Veech, Teichmuller curves in modular space, Eisenstein series, and an application to triangular billiards, Inv. Math. 97 ( 1989), 553-583. | MR | Zbl

[23] W. Veech, The billiard in the regular polygon, Geom. and Func. Analysis 2 ( 1992), 341-379. | MR | Zbl

[24] W. A. Veech, Flat surfaces, Amer. J. Math. 15 ( 1993), 589-689. | MR | Zbl

[25] A. B. Venkov, The spectral theory of'automorphic fonctions, Kluwer, Amsterdam, 1990.

[26] Y. Vorobets, Structures plates et billards dans les polygones rationnels, Uspekhi Mat. Nauk 51 ( 1996), 145-146 (en russe). | MR | Zbl

[27] C. Ward, Fuchsian groups and polygonal billiards, Ph. D. Dissertation, Rice University, 1996.

[28] C. Ward, Calculation of Fuchsian groups associated to rational triangles, preprint, Rice University, 1996.

[29] A. Zemlyakov and A. Katok, Topological transitivity of billiards in polygons, Math. Notes 18 ( 1976), 760-764. | Zbl