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
topGuivarc'h, Y., and Le Jan, Y.. "Asymptotic winding of the geodesic flow on modular surfaces and continuous fractions." Annales scientifiques de l'École Normale Supérieure 26.1 (1993): 23-50. <http://eudml.org/doc/82335>.
@article{Guivarch1993,
author = {Guivarc'h, Y., Le Jan, Y.},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {degenerate probability laws; windings of a two-dimensional Brownian motion; modular surfaces; compact Riemann surface; geodesic flow; Cauchy laws},
language = {eng},
number = {1},
pages = {23-50},
publisher = {Elsevier},
title = {Asymptotic winding of the geodesic flow on modular surfaces and continuous fractions},
url = {http://eudml.org/doc/82335},
volume = {26},
year = {1993},
}
TY - JOUR
AU - Guivarc'h, Y.
AU - Le Jan, Y.
TI - Asymptotic winding of the geodesic flow on modular surfaces and continuous fractions
JO - Annales scientifiques de l'École Normale Supérieure
PY - 1993
PB - Elsevier
VL - 26
IS - 1
SP - 23
EP - 50
LA - eng
KW - degenerate probability laws; windings of a two-dimensional Brownian motion; modular surfaces; compact Riemann surface; geodesic flow; Cauchy laws
UR - http://eudml.org/doc/82335
ER -
References
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
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.