Asymptotic winding of the geodesic flow on modular surfaces and continuous fractions

Y. Guivarc'h; Y. Le Jan

Annales scientifiques de l'École Normale Supérieure (1993)

  • Volume: 26, Issue: 1, page 23-50
  • ISSN: 0012-9593

How to cite

top

Guivarc'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
  1. [Die] J. DIEUDONNÉ, Éléments d'analyse 9, Gauthier-Villars, Paris, 1982. 
  2. [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
  3. [H] S. HU, Homotopy Theory, Academy Press, 1959. MR21 #5186
  4. [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
  5. [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
  6. [HW] G. HARDY and E. M. WRIGHT, An Introduction to the Theory of Numbers, University Press, Oxford, 1975. 
  7. [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
  8. [Ka] T. KATO, Perturbation Theory for Linear Operators, Springer, Berlin, Heidelberg, New York, 1976. Zbl0342.47009MR53 #11389
  9. [KS] A. KATSUDA and T. SUNADA, Closed Orbits in Homology Classes (Pub. Math. I.H.E.S., Vol. 71, 1990). Zbl0728.58026MR92m:58102
  10. [LeH] J. LEHNER, Discontinuous Groups and Automorphic Functions (A.M.S., Providence, 1964). Zbl0178.42902MR29 #1332
  11. [L] P. LÉVY, Fractions continues aléatoires (Rend. Circ. Math. Palermo, 1952, pp. 1-39). Zbl0048.36101MR16,600e
  12. [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
  13. [N] F. NORMAN, Markov Processes and Learning Model (Academic press, 1972). Zbl0262.92003
  14. [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
  15. [RY] D. REVUZ and M. YOR, Continuous Martingale Calculus and Brownian Motion (to appear). 
  16. [Sch] B. SCHOENBERG, Elliptic Modular Functions, Springer, Berlin, Heidelberg, New York, 1974. 
  17. [Se] C. SERIES, The Modular Surface and Continued Fractions (J. London Math. Soc., Vol. 31, 1985, pp. 69-80). Zbl0545.30001MR87c:58094
  18. [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
  19. [Spi] F. SPITZER, Some Theorems Concerning Two Dimensional Brownian Motion (Trans. Ann. Math. Soc., Vol. 87, 1958, pp. 187-197). Zbl0089.13601MR21 #3051
  20. [Spr] G. SPRINGER, Introduction to Rieman Surfaces, Addison-Wesley (Reading, 1957). Zbl0078.06602MR19,1169g
  21. [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
  1. Y. Guivarch, Y. Le Jan, Note rectificative : “Asymptotic winding of the geodesic flow on modular surfaces and continuous fractions”
  2. Anne Broise, Fractions continues multidimensionnelles et lois stables
  3. Françoise Dal'bo, Marc Peigné, Groupes du ping-pong et géodésiques fermées en courbure -1
  4. Nathanaël Enriquez, Jacques Franchi, Masse des pointes, temps de retour et enroulements en courbure négative
  5. Viviane Baladi, Aïcha Hachemi, A local limit theorem with speed of convergence for euclidean algorithms and diophantine costs
  6. Sébastien Blachère, Peter Haïssinsky, Pierre Mathieu, Harmonic measures versus quasiconformal measures for hyperbolic groups
  7. Martine Babillot, Marc Peigné, Homologie des géodésiques fermées sur des variétés hyperboliques avec bouts cuspidaux
  8. Marc Peigné, Iterated Function Systems and Spectral Decomposition of the Associated Markov Operator
  9. Martine Babillot, Marc Peigné, Asymptotic laws for geodesic homology on hyperbolic manifolds with cusps
  10. Loïc Hervé, Françoise Pène, The Nagaev-Guivarc’h method via the Keller-Liverani theorem

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.