Homologie des géodésiques fermées sur des variétés hyperboliques avec bouts cuspidaux

Martine Babillot; Marc Peigné

Annales scientifiques de l'École Normale Supérieure (2000)

  • Volume: 33, Issue: 1, page 81-120
  • ISSN: 0012-9593

How to cite

top

Babillot, Martine, and Peigné, Marc. "Homologie des géodésiques fermées sur des variétés hyperboliques avec bouts cuspidaux." Annales scientifiques de l'École Normale Supérieure 33.1 (2000): 81-120. <http://eudml.org/doc/82511>.

@article{Babillot2000,
author = {Babillot, Martine, Peigné, Marc},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {hyperbolic manifolds; cuspidal ends; complete Riemannian manifold; growth rate; number of closed geodesics; fixed homology class},
language = {fre},
number = {1},
pages = {81-120},
publisher = {Elsevier},
title = {Homologie des géodésiques fermées sur des variétés hyperboliques avec bouts cuspidaux},
url = {http://eudml.org/doc/82511},
volume = {33},
year = {2000},
}

TY - JOUR
AU - Babillot, Martine
AU - Peigné, Marc
TI - Homologie des géodésiques fermées sur des variétés hyperboliques avec bouts cuspidaux
JO - Annales scientifiques de l'École Normale Supérieure
PY - 2000
PB - Elsevier
VL - 33
IS - 1
SP - 81
EP - 120
LA - fre
KW - hyperbolic manifolds; cuspidal ends; complete Riemannian manifold; growth rate; number of closed geodesics; fixed homology class
UR - http://eudml.org/doc/82511
ER -

References

top
  1. [1] T. AKAZA, 3/2-dimensional measure of singular sets of some Kleinian groups, J. Math. Soc. Japan 24 (1972) 448-464. Zbl0235.30020MR46 #9338
  2. [2] E. ARTIN, Ein mechanisches System mit quasiergodischen Bahnen, in : Collected Papers, Addison-Wesley, 1965, pp. 499-501. 
  3. [3] T. ADACHI and T. SUNADA, Homology of closed geodesics in a negatively curved manifold, J. Differential Geom. 26 (1987) 81-99. Zbl0618.58028MR88g:58149
  4. [4] A. BROISE, F. DAL'BO and M. PEIGNÉ, Méthode des opérateurs de transfert : transformations dilatantes de l'intervalle et dénombrement de géodésiques fermées, Soc. Math. France, Astérisque 238, 1996. Zbl0988.37032
  5. [5] A.F. BEARDON, The exponent of convergence of Poincaré series, Proc. London Math. Soc. 3 (18) (1968) 461-483. Zbl0162.38801MR37 #2986
  6. [6] V. BALADI and G. KELLER, Zeta functions and transfer operators for piecewise monotone transformations, Comm. Math. Phys. 127 (1990) 459-477. Zbl0703.58048MR91b:58196
  7. [7] M. BABILLOT and F. LEDRAPPIER, Lalley's theorem on periodic orbits of hyperbolic flows, Ergodic Theory Dynamical Systems 18 (1998) 17-39. Zbl0915.58074MR99a:58128
  8. [8] R. BOWEN, The equidistribution of closed geodesics, Amer. J. Math. 94 (1972) 413-423. Zbl0249.53033MR47 #4291
  9. [9] R. BOWEN, Hausdorff dimension of quasi-circles, Publ. Math. IHES 50 (1979). Zbl0439.30032MR81g:57023
  10. [10] M. BABILLOT and M. PEIGNÉ, Closed geodesics in homology classes on hyperbolic manifolds with cusps, C. R. Acad. Sci. Paris Série I 324 (1997) 901-906. Zbl0884.58078MR99a:58121
  11. [11] L. BREIMAN, Probability, Addison-Wesley, 1968. Zbl0174.48801MR37 #4841
  12. [12] X. BRESSAUD, Opérateurs de transfert sur le décalage à alphabet infini et applications, Thèse de l'Université Paris 6, 1996. 
  13. [13] R. BOWEN and C. SERIES, Markov maps associated with Fuchsian groups, Publ. Math. IHES 50 (1979) 153-170. Zbl0439.30033MR81b:58026
  14. [14] W. DOEBLIN and R. FORTET, Sur les chaines à liaison complètes, Bull. Soc. Math. France 65 (1937) 132-148. Zbl0018.03303JFM63.1077.05
  15. [15] P.G. DOYLE, On the bass note of a Schottky group, Acta Math. 160 (1988) 249-284. Zbl0649.30036MR90b:30053
  16. [16] F. DAL'BO and M. PEIGNÉ, Groupes du ping-pong et géodésiques fermées en courbure -1, Ann. Inst. Fourier 46 (3) (1996) 755-799. Zbl0853.53032MR97h:58126
  17. [17] N. ENRIQUEZ, J. FRANCHI and Y. LE JAN, Stable windings for geodesics under Patterson-Sullivan measure, Prépublication 431 du Laboratoire de Probabilités de l'Université Paris VI, 1998. Zbl0932.37013
  18. [18] N. ENRIQUEZ and Y. LE JAN, Statistic of the winding of geodesics on a Riemann surface with finite area and constant negative curvature, Rev. Mat. Iber. 13 (1997) 377-401. Zbl0907.58054MR99f:58221
  19. [19] C. EPSTEIN, Asymptotics for closed geodesics in a homology class-the finite volume case, Duke Math. J. 55 (1987) 717-757. Zbl0648.58041MR89c:58098
  20. [20] J. FRANCHI, Asymptotic singular homology of a complete hyperbolic 3-manifold of finite volume, Proc. London Math. Soc. 79 (1999) 451-480. Zbl1056.58012MR2001a:58051
  21. [21] Y. GUIVARC'H and Y. LE JAN, Asymptotic winding of the geodesic flow on modular surfaces and continued fractions, Ann. Sci. ENS 26 (1993) 23-50. Zbl0784.60076MR94a:58157
  22. [22] L. GUILLOPÉ, Fonctions Zêta de Selberg et surfaces de géométrie finie, Adv. Studies in Pure Math. 21 (1992) 33-72. Zbl0794.58044MR94d:11032
  23. [23] Y. GUIVARC'H and J. HARDY, Théorèmes limites pour une classe de chaînes de Markov, et applications aux difféomorphismes d'Anosov, Ann. IHP 24 73-98. Zbl0649.60041MR89m:60080
  24. [24] N.T.A. HAYDN, Meromorphic extensions of the Zeta function for Axiom A flows, Ergodic Theory Dynamical Systems 10 (1990) 347-360. Zbl0694.58035MR91g:58219
  25. [25] D. HEIJHAL, The Selberg trace formula and the Riemann Zeta function, Duke Math. J. 43 (1976) 441-482. Zbl0346.10010MR54 #2591
  26. [26] H. HENNION, Sur un théorème spectral et son application aux noyaux Lipschitziens, Proc. AMS 118 (1993) 637-634. Zbl0772.60049MR93g:60141
  27. [27] H. HUBER, Zur analytischen Theorie hyperbolischer Raumformen und Bewegungsgruppen (I), Math. Ann. 138 (1959) 1-26 ; (II), Math. Ann. 142 (1961) 385-398 ; (III), Math. Ann. 143 (1961) 463-464. Zbl0101.05702MR27 #4923
  28. [28] S. ISOLA, On the rate of convergence to equilibrium of countable ergodic Markov chains, Prépublication, Università degli Studi di Bologna, 1997. 
  29. [29] S. ISOLA, Dynamical Zeta functions and correlation functions for intermittent interval maps, Prépublication, Università degli Studi di Bologna, 1997. 
  30. [30] S. ISOLA, Renewal sequences and intermittency, Prépublication, Università degli Studi di Bologna, 1997. 
  31. [31] A. KATSUDA and T. SUNADA, Closed orbits in homology classes, Publ. Math. IHES 71 (1990) 5-32. Zbl0728.58026MR92m:58102
  32. [32] S. LALLEY, Renewal theorems in symbolic dynamics with applications to geodesic flows, non euclidean tesselations and their fractal limits, Acta Math. 163 (1989) 1-55. Zbl0701.58021MR91c:58112
  33. [33] S. LALLEY, Closed geodesics in homology classes on surfaces of variable negative curvature, Duke Math. J. 58 (1989) 795-821. Zbl0732.53035MR91a:58143
  34. [34] S. LALLEY, Probabilistic methods in certain counting problems in ergodic theory, in : T. Bedford, M. Keane and C. Series, eds., Ergodic Theory, Symbolic Dynamics and Hyperbolic Spaces, Oxford University Press, Oxford, 1991. Zbl0756.58032MR1130178
  35. [35] B. MASKITT, Kleinian Groups, Springer, Berlin, 1988. Zbl0627.30039
  36. [36] G.A. MARGULIS, Applications of ergodic theory for the investigation of manifolds of negative curvature, Func. Anal. Appl. 3 (1969) 335-336. Zbl0207.20305MR41 #2582
  37. [37] C. MCMULLEN, Hausdorff dimension and conformal dynamics, I : Kleinian Groups and strong limits, à paraître J. Diff. Geom. III : Computation of dimension, Amer. J. Math. 120 (1998) 691-721. Zbl0953.30026MR2000d:37055
  38. [38] R. MIATELLO and N.R. WALLACH, The resolvant of the Laplacian on locally symmetric spaces, J. Differential Geom. 36 (1992) 663-698. Zbl0766.53044MR93i:58160
  39. [39] W. PARRY, An analogue of the prime number theorem for closed orbits of shifts of finite type and their suspensions, Israel J. Math. 45 (1983) 573-591. Zbl0552.28020MR85c:58089
  40. [40] S.J. PATTERSON, The limit set of a Fuchsian group, Acta Math. 136 (1976) 241-273. Zbl0336.30005MR56 #8841
  41. [41] M. POLLICOTT, Homology and closed geodesics in a compact negatively curved surface, Amer. J. Math. 113 (1991) 379-385. Zbl0728.53031MR92e:58158
  42. [42] W. PARRY and M. POLLICOTT, Zeta functions and the periodic orbit structure of hyperbolic dynamics, Astérisque 187-188, Soc. Math. France, 1990. Zbl0726.58003MR92f:58141
  43. [43] R. PHILLIPS and P. SARNAK, Geodesics in homology classes, Duke Math. J. 55 (1987) 287-297. Zbl0642.53050MR88g:58151
  44. [44] T. PRELLBERG and J. SLAWNY, Maps of intervals with indifferent fixed points : thermodynamic formalism and phase transitions, J. Stat. Phys. 66 (1992) 503-514. Zbl0892.58024MR93g:58085
  45. [45] J.G. RATCLIFFE, Foundations of Hyperbolic Geometry, Springer, New York, 1994. Zbl0809.51001
  46. [46] T. ROBLIN, Sur la théorie ergodique des groupes discrets en géométrie hyperbolique, Thèse de doctorat de l'Université Paris XI, 1999. 
  47. [47] J. ROUSSEAU-EGELE, Un théorème de la limite locale pour une classe de fonctions dilatantes et monotones par morceaux, Ann. Probab. 11 (1983) 772-788. Zbl0518.60033MR84m:60032
  48. [48] W. RUDIN, Analyse Réelle et Complexe, Masson, Paris, 1975. Zbl0333.28001MR52 #10292
  49. [49] H.H. RUGH, Intermittency and regularized Fredholm determinants, Invent. Math. 135 (1999) 1-24. Zbl0988.37027MR2000c:37025
  50. [50] A. SELBERG, Harmonic analysis and discontinuous groups in weakly symmetric spaces with applications to Dirichlet series, J. Indian Math. Soc. 20 (1956) 47-87. Zbl0072.08201MR19,531g
  51. [51] C. SERIES, The modular surface and continued fractions, J. London Math. Soc. 31 (1985) 69-80. Zbl0545.30001MR87c:58094
  52. [52] R. SHARP, Closed orbits in homology classes for Anosov flows, Ergodic Theory Dynamical Systems 13 (1993) 387-408. Zbl0783.58059MR94g:58169
  53. [53] F. SPITZER, Principles of Random Walks, Van Nostrand, Princeton, 1964. Zbl0119.34304MR30 #1521
  54. [54] D. SULLIVAN, The density at infinity of a discrete group of hyperbolic isometries, Publ. Math. IHES 50 (1979) 171-209. Zbl0439.30034MR81b:58031
  55. [55] D. SULLIVAN, Entropy, Hausdorff measure old and new, and limit sets of geometrically finite Kleinian groups, Acta Math. 153 (1984) 259-277. Zbl0566.58022MR86c:58093
  56. [56] L.S. YOUNG, Recurrence times and rates of mixing, à paraître, Israel J. Math. (1999). Zbl0983.37005MR2001j:37062
  57. [57] S. ZELDITCH, Trace formula for compact Γ2(R) and the equidistribution theory of closed geodesics, Duke Math. J. 59 (1989) 27-81. Zbl0686.10024MR91d:11056

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.