no. 6
Affine diffeomorphisms of translation surfaces : periodic points, fuchsian groups, and arithmeticity
Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 36 (2003) no. 6, pp. 847-866. 
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     author = {Gutkin, Eugene and Hubert, Pascal and Schmidt, Thomas A.},
     title = {Affine diffeomorphisms of translation surfaces : periodic points, fuchsian groups, and arithmeticity},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     pages = {847--866},
     publisher = {Elsevier},
     volume = {Ser. 4, 36},
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     year = {2003},
     doi = {10.1016/j.ansens.2003.05.001},
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     zbl = {1106.37018},
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     url = {http://www.numdam.org/articles/10.1016/j.ansens.2003.05.001/}
}
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Gutkin, Eugene; Hubert, Pascal; Schmidt, Thomas A. Affine diffeomorphisms of translation surfaces : periodic points, fuchsian groups, and arithmeticity. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 36 (2003) no. 6, pp. 847-866. doi : 10.1016/j.ansens.2003.05.001. http://www.numdam.org/articles/10.1016/j.ansens.2003.05.001/

[1] Arnoux P., Hubert P., Fractions continues sur les surfaces de Veech, J. Anal. Math. 81 (2000) 35-64. | MR | Zbl

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

[3] Earle C.J., Gardiner F.P., Teichmüller disks and Veech's F structures, Extremal Riemann Surfaces, in: Contemp. Math., vol. 201, Amer. Math. Soc, Providence, RI, 1997, pp. 165-189. | MR | Zbl

[4] Eskin A., Masur H., Asymptotic formulas on flat surfaces, Ergodic Theory Dynam. Systems 21 (2001) 443-478. | MR | Zbl

[5] Farkas H.M., Kra I., Riemann Surfaces, 2nd Edition, Grad. Texts in Math., vol. 71, Springer-Verlag, Berlin, 1992. | MR | Zbl

[6] Fox R.H., Kershner R.B., Concerning the transitive properties of geodesics on a rational polyhedron, Duke Math. J. 2 (1936) 147-150. | JFM | MR

[7] Gutkin E., Billiard flows on almost integrable polyhedral surfaces, Ergodic Theory Dynam. Systems 4 (1984) 569-584. | MR | Zbl

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

[9] Gutkin E., Branched coverings and closed geodesies in flat surfaces, with applications to billiards, in: Gambaudo J.-M., Hubert P., Tisseur P., Vaienti S. (Eds.), Dynamical Systems from Crystal to Chaos, World Scientific, Singapore, 2000, pp. 259-273. | MR

[10] Gutkin E., Judge C., The geometry and arithmetic of translation surfaces with applications to polygonal billiards, Math. Res. Lett. 3 (1996) 391-403. | MR | Zbl

[11] Gutkin E., Judge C., Affine mappings of translation surfaces: Geometry and arithmetic, Duke Math. J. 103 (2000) 191-213. | MR | Zbl

[12] Hubbard J., Masur H., Quadratic differentials and foliations, Acta Math. 142 (1979) 221-274. | MR | Zbl

[13] Hardy G.H., Wright E.M., An Introduction to the Theory of Numbers, Oxford Univ. Press, London, 1938. | MR | Zbl

[14] Hubert P., Schmidt T.A., Veech groups and polygonal coverings, J. Geom. Phys. 35 (2000) 75-91. | MR | Zbl

[15] Hubert P., Schmidt T.A., Invariants of translation surfaces, Ann. Inst. Fourier 51 (2001) 461-495. | Numdam | MR | Zbl

[16] Katok A., Zemlyakov A., Topological transitivity of billiards in polygons, Math. Notes 18 (1975) 760-764. | MR | Zbl

[17] Kenyon R., Smillie J., Billiards in rational-angled triangles, Comment. Math. Helv. 75 (2000) 65-108. | MR | Zbl

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

[19] Masur H., Tabachnikov S., Rational billiards and flat structures, in: Handbook on Dynamical Systems, vol. 1A, Elsevier, Amsterdam, 2002, pp. 1015-1090. | MR | Zbl

[20] Puchta J.-Ch., On triangular billiards, Comment. Math. Helv. 76 (2001) 501-505. | MR | Zbl

[21] Schmoll M., On the asymptotic quadratic growth rate of saddle connections and periodic orbits on marked flat tori, Geom. Funct. Anal. (GAFA) 12 (2002) 622-649. | MR | Zbl

[22] Stäckel P., Geodätische Linien auf Polyederflächen, Rend. Circ. Mat. Palermo 22 (1906) 141-151. | JFM

[23] Thurston W., On the geometry and dynamics of diffeomorphisms of surfaces, Bull. Amer. Math. Soc. 19 (1988) 417-431. | MR | Zbl

[24] Veech W.A., Dynamical systems on analytic manifolds of quadratic differentials, Preprint, 1984.

[25] Veech W.A., The Teichmüller geodesic flow, Ann. of Math. 124 (1986) 441-530. | MR | Zbl

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

[27] Veech W.A., The billiard in a regular polygon, Geom. Func. Anal. (GAFA) 2 (1992) 341-379. | MR | Zbl

[28] Veech W.A., Geometric realizations of hyperelliptic curves, in: Algorithms, Fractals, and Dynamics, Okayama/Kyoto, 1992, Plenum, New York, 1995, pp. 217-226. | MR | Zbl

[29] Vorobets Ya., Plane structures and billiards in rational polygons: the Veech alternative, Russian Math. Surveys 51 (1996) 779-817. | MR | Zbl

[30] Ward C., Calculation of Fuchsian groups associated to billiards in a rational triangle, Ergodic Theory Dynam. Systems 18 (1998) 1019-1042. | MR | Zbl

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