Asymptotic winding of the geodesic flow on modular surfaces and continuous fractions
Annales scientifiques de l'École Normale Supérieure (1993)
- Volume: 26, Issue: 1, page 23-50
- ISSN: 0012-9593
Access Full Article
topHow to cite
topReferences
top- [Die] J. DIEUDONNÉ, Éléments d'analyse 9, Gauthier-Villars, Paris, 1982.
- [F] J. FRANCHI, Théorèmes des résidus asymptotiques pour le mouvement Brownien sur une surface riemannienne compacte (Ann. I.H.P., Vol. 27, 1991, pp. 445-462). Zbl0746.60059MR92k:60112
- [H] S. HU, Homotopy Theory, Academy Press, 1959. MR21 #5186
- [G] Y. GUIVARC'H and G. HARDY, Théorèmes limites pour une classe de chaînes de Markov et applications aux difféomorphismes d'Anosov (Ann. I.H.P., Vol. 24, 1988, pp. 73-98). Zbl0649.60041MR89m:60080
- [GL] Y. GUIVARC'H and Y. LE JAN, Sur l'enroulement du flot géodésique (C.R. Ac. Sc. Paris, T. 311, Série I, 1990, pp. 645-648). Zbl0727.58033MR92b:58175
- [HW] G. HARDY and E. M. WRIGHT, An Introduction to the Theory of Numbers, University Press, Oxford, 1975.
- [JK] A. JAKUBOWSKI and M. KOBUS, α-Stable Limit Theorems for Sums of Dependent Random Vectors (J. Mult. Analysis, Vol. 29, 1989, pp. 219-251). Zbl0687.60025MR91a:60065
- [Ka] T. KATO, Perturbation Theory for Linear Operators, Springer, Berlin, Heidelberg, New York, 1976. Zbl0342.47009MR53 #11389
- [KS] A. KATSUDA and T. SUNADA, Closed Orbits in Homology Classes (Pub. Math. I.H.E.S., Vol. 71, 1990). Zbl0728.58026MR92m:58102
- [LeH] J. LEHNER, Discontinuous Groups and Automorphic Functions (A.M.S., Providence, 1964). Zbl0178.42902MR29 #1332
- [L] P. LÉVY, Fractions continues aléatoires (Rend. Circ. Math. Palermo, 1952, pp. 1-39). Zbl0048.36101MR16,600e
- [LM] T. LYONS and H. P. MC KEAN, Windings of the Plane Brownian Motion, (Advances in Maths, Vol. 51, 1984, pp. 212-225). Zbl0541.60075MR85k:60114b
- [N] F. NORMAN, Markov Processes and Learning Model (Academic press, 1972). Zbl0262.92003
- [Rat] M. RATNER, The Central Limit Theorem for Geodesic Flows on n Dimensional Manifolds of Negative Curvature (Israël J. of Math., Vol. 16, 1973, pp. 180-197). Zbl0283.58010MR48 #11446
- [RY] D. REVUZ and M. YOR, Continuous Martingale Calculus and Brownian Motion (to appear).
- [Sch] B. SCHOENBERG, Elliptic Modular Functions, Springer, Berlin, Heidelberg, New York, 1974.
- [Se] C. SERIES, The Modular Surface and Continued Fractions (J. London Math. Soc., Vol. 31, 1985, pp. 69-80). Zbl0545.30001MR87c:58094
- [Si] Y. G. SINAÏ, The Central Limit Theorem for Geodesic Flows on Manifolds of Constant Negative Curvature (Dokl. Akad. Nauk SSSR, Vol. 133, 1960, pp. 1303-1306). Zbl0129.31103MR23 #A2906
- [Spi] F. SPITZER, Some Theorems Concerning Two Dimensional Brownian Motion (Trans. Ann. Math. Soc., Vol. 87, 1958, pp. 187-197). Zbl0089.13601MR21 #3051
- [Spr] G. SPRINGER, Introduction to Rieman Surfaces, Addison-Wesley (Reading, 1957). Zbl0078.06602MR19,1169g
- [Su] SULLIVAN, Disjoint Spheres, Approximation by Imaginary Quadratic Numbers and the Logarithm Law for Geodesics, (Acta Math., Vol. 149, 1983, pp. 123-237). Zbl0517.58028MR84j:58097
Citations in EuDML Documents
top- Y. Guivarch, Y. Le Jan, Note rectificative : “Asymptotic winding of the geodesic flow on modular surfaces and continuous fractions”
- Anne Broise, Fractions continues multidimensionnelles et lois stables
- Françoise Dal'bo, Marc Peigné, Groupes du ping-pong et géodésiques fermées en courbure -1
- Nathanaël Enriquez, Jacques Franchi, Masse des pointes, temps de retour et enroulements en courbure négative
- Viviane Baladi, Aïcha Hachemi, A local limit theorem with speed of convergence for euclidean algorithms and diophantine costs
- Sébastien Blachère, Peter Haïssinsky, Pierre Mathieu, Harmonic measures versus quasiconformal measures for hyperbolic groups
- Martine Babillot, Marc Peigné, Homologie des géodésiques fermées sur des variétés hyperboliques avec bouts cuspidaux
- Marc Peigné, Iterated Function Systems and Spectral Decomposition of the Associated Markov Operator
- Martine Babillot, Marc Peigné, Asymptotic laws for geodesic homology on hyperbolic manifolds with cusps
- Loïc Hervé, Françoise Pène, The Nagaev-Guivarc’h method via the Keller-Liverani theorem