Geodesic
Transitivity Properties of Fuchsian Groups
Canadian journal of mathematics, Tome 28 (1976) no. 4, pp. 805-814

Voir la notice de l'article provenant de la source Cambridge University Press

A Fuchsian group G is a discrete group of fractional linear transforms each of which preserve a disc (or half plane). We consider only groups which preserve the unit disc Δ = {z: |z| < 1} and none of whose transforms, except the identity, fix infinity (any Fuchsian group is conjugate to such a group). 
Nicholls, Peter J. Transitivity Properties of Fuchsian Groups. Canadian journal of mathematics, Tome 28 (1976) no. 4, pp. 805-814. doi: 10.4153/CJM-1976-077-8
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[1] 1. Ahlfors, L. V., Remarks on the classification of open Riemann surfaces, Ann. Acad. Sci. Fenn. Ser. A.l. 87 (1951). Google Scholar

[2] 2. Artin, E., Ein mechanische System mit quasiergodischen Bahnen, Abh. Math. Sem. Univ. Hamburg S (1924), 170–175. Google Scholar

[3] 3. Beardon, A. F. and Maskit, B., Limit points of Kleinian groups and finite sided fundamental polyhedra, Acta Math. 132 (1974), 1–12. Google Scholar

[4] 4. Ford, L. R., Automorphic functions (Chelsea, New York, 1951). Google Scholar

[5] 5. Hedlund, G. A., Fuchsian groups and transitive horocycles, Duke Math. J. 2 (1936), 530–542. Google Scholar

[6] 6. Hedlund, G. A., A new pr∞f for a metrically transitive system, Amer. J. Math. 62 (1940), 233–242. Google Scholar

[7] 7. Hopf, E., Fuchsian groups and ergodic theory, Trans. Amer. Math. Soc. 39 (1936), 299–314. Google Scholar

[8] 8. Hopf, E., Statistik der geodatischen Linien in Mannigfaltigkeiten negativer Krummung, Ber. Verh. Sachs. Akad. Wiss. Leipzig 91 (1939), 261–304. Google Scholar

[9] 9. Hopf, E., Ergodic theory and the geodesic flow on surfaces of constant negative curvature, Bull. Amer. Math. Soc. 77 (1971), 863–877. Google Scholar

[10] 10. Koebe, P., Riemannsche Mannigfaltigkeiten una nicht euklidische Raumformen VI, S.-B. Deutsch. Akad. Wiss. Berlin. Kl. Math. Phys. Tech. (1930), 504–541. Google Scholar

[11] 11. Lehner, J., Discontinuous groups and automorphic functions, Math. Survey 8 (Amer. Math. Soc, Providence, 1964). Google Scholar

[12] 12. Myberg, P. J., Einige Anwendungen der Kettenbriiche in der Théorie der bindren quadratischen Formen und der elliptischen Modulfunktionen, Ann. Acad. Sci. Fenn. Ser. A.l. 23 (1925). Google Scholar

[13] 13. Myberg, P. J., Ein Approximationssatz fiir die Fuchssen Gruppen, i\cta Math. 57 (1931), 389–409. Google Scholar

[14] 14. Nicholls, P. J., Special limit points for Fuchsian groups and automorphic functions near the limit set, Indiana U. Math. J. 24 (1974), 143–148. Google Scholar

[15] 15. Nicholls, P. J., Transitive horocycles for Fuchsian groups, Duke Math. J. 1-2 (1975), 307–312. Google Scholar

[16] 16. Patterson, S. J., A lattice point problem in hyperbolic space, Mathematika 22 (1975), 81–88. Google Scholar

[17] 17. Patterson, S. J., Spectral theory and Fuchsian groups, to appear. Google Scholar

[18] 18. Pommerenke, Ch., On the Green s function of Fuchsian groups, to appear. Google Scholar

[19] 19. Sario, L. and Nakai, M., Classification theory of Riemann surfaces, (Springer-Verlag, New York, 1970). Google Scholar

[20] 20. Seidel, Y., On a metric property of Fuchsian groups, Proc. Nat. Acad. Sci. U.S.A. 21 (1935), 475–478. Google Scholar

[21] 21. Shimada, S., On P. J. Myrbergf s approximation theorem on Fuchsian groups, Mem. Coll. Sci., Kyoto U. Ser. A. 33 (1960), 231–241. Google Scholar

[22] 22. Tsuji, M., On Hopf s ergodic theorem, Jap. J. Math. 19 (1945), 259–284. Google Scholar

[23] 23. Tsuji, M., Potential theory in modern function theory (Maruzen, Tokyo, 1959). Google Scholar

[24] 24. Yujobo, Z., A theorem on Fuchsian groups, Math. Jap. 1 (1949), 168–169. Google Scholar

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