@article{ASENS_2000_4_33_1_81_0, author = {Babillot, Martine and Peign\'e, Marc}, title = {Homologie des g\'eod\'esiques ferm\'ees sur des vari\'et\'es hyperboliques avec bouts cuspidaux}, journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure}, pages = {81--120}, publisher = {Elsevier}, volume = {4e s{\'e}rie, 33}, number = {1}, year = {2000}, doi = {10.1016/s0012-9593(00)00104-x}, mrnumber = {2001b:37043}, zbl = {0984.37033}, language = {fr}, url = {http://www.numdam.org/articles/10.1016/s0012-9593(00)00104-x/} }
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 SP - 81 EP - 120 VL - 33 IS - 1 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/s0012-9593(00)00104-x/ DO - 10.1016/s0012-9593(00)00104-x LA - fr ID - ASENS_2000_4_33_1_81_0 ER -
%0 Journal Article %A Babillot, Martine %A Peigné, Marc %T Homologie des géodésiques fermées sur des variétés hyperboliques avec bouts cuspidaux %J Annales scientifiques de l'École Normale Supérieure %D 2000 %P 81-120 %V 33 %N 1 %I Elsevier %U http://www.numdam.org/articles/10.1016/s0012-9593(00)00104-x/ %R 10.1016/s0012-9593(00)00104-x %G fr %F ASENS_2000_4_33_1_81_0
Babillot, Martine; Peigné, Marc. Homologie des géodésiques fermées sur des variétés hyperboliques avec bouts cuspidaux. Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 33 (2000) no. 1, pp. 81-120. doi : 10.1016/s0012-9593(00)00104-x. http://www.numdam.org/articles/10.1016/s0012-9593(00)00104-x/
[1] 3/2-dimensional measure of singular sets of some Kleinian groups, J. Math. Soc. Japan 24 (1972) 448-464. | MR | Zbl
,[2] Ein mechanisches System mit quasiergodischen Bahnen, in : Collected Papers, Addison-Wesley, 1965, pp. 499-501.
,[3] Homology of closed geodesics in a negatively curved manifold, J. Differential Geom. 26 (1987) 81-99. | MR | Zbl
and ,[4] Méthode des opérateurs de transfert : transformations dilatantes de l'intervalle et dénombrement de géodésiques fermées, Soc. Math. France, Astérisque 238, 1996. | Zbl
, and ,[5] The exponent of convergence of Poincaré series, Proc. London Math. Soc. 3 (18) (1968) 461-483. | MR | Zbl
,[6] Zeta functions and transfer operators for piecewise monotone transformations, Comm. Math. Phys. 127 (1990) 459-477. | MR | Zbl
and ,[7] Lalley's theorem on periodic orbits of hyperbolic flows, Ergodic Theory Dynamical Systems 18 (1998) 17-39. | MR | Zbl
and ,[8] The equidistribution of closed geodesics, Amer. J. Math. 94 (1972) 413-423. | MR | Zbl
,[9] Hausdorff dimension of quasi-circles, Publ. Math. IHES 50 (1979). | Numdam | MR | Zbl
,[10] Closed geodesics in homology classes on hyperbolic manifolds with cusps, C. R. Acad. Sci. Paris Série I 324 (1997) 901-906. | MR | Zbl
and ,[11] Probability, Addison-Wesley, 1968. | MR | Zbl
,[12] Opérateurs de transfert sur le décalage à alphabet infini et applications, Thèse de l'Université Paris 6, 1996.
,[13] Markov maps associated with Fuchsian groups, Publ. Math. IHES 50 (1979) 153-170. | Numdam | MR | Zbl
and ,[14] Sur les chaines à liaison complètes, Bull. Soc. Math. France 65 (1937) 132-148. | JFM | Numdam | Zbl
and ,[15] On the bass note of a Schottky group, Acta Math. 160 (1988) 249-284. | MR | Zbl
,[16] Groupes du ping-pong et géodésiques fermées en courbure -1, Ann. Inst. Fourier 46 (3) (1996) 755-799. | Numdam | MR | Zbl
and ,[17] Stable windings for geodesics under Patterson-Sullivan measure, Prépublication 431 du Laboratoire de Probabilités de l'Université Paris VI, 1998.
, and ,[18] Statistic of the winding of geodesics on a Riemann surface with finite area and constant negative curvature, Rev. Mat. Iber. 13 (1997) 377-401. | MR | Zbl
and ,[19] Asymptotics for closed geodesics in a homology class-the finite volume case, Duke Math. J. 55 (1987) 717-757. | MR | Zbl
,[20] Asymptotic singular homology of a complete hyperbolic 3-manifold of finite volume, Proc. London Math. Soc. 79 (1999) 451-480. | MR | Zbl
,[21] Asymptotic winding of the geodesic flow on modular surfaces and continued fractions, Ann. Sci. ENS 26 (1993) 23-50. | Numdam | MR | Zbl
and ,[22] Fonctions Zêta de Selberg et surfaces de géométrie finie, Adv. Studies in Pure Math. 21 (1992) 33-72. | MR | Zbl
,[23] Théorèmes limites pour une classe de chaînes de Markov, et applications aux difféomorphismes d'Anosov, Ann. IHP 24 73-98. | Numdam | MR | Zbl
and ,[24] Meromorphic extensions of the Zeta function for Axiom A flows, Ergodic Theory Dynamical Systems 10 (1990) 347-360. | MR | Zbl
,[25] The Selberg trace formula and the Riemann Zeta function, Duke Math. J. 43 (1976) 441-482. | MR | Zbl
,[26] Sur un théorème spectral et son application aux noyaux Lipschitziens, Proc. AMS 118 (1993) 637-634. | MR | Zbl
,[27] 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. | MR | Zbl
,[28] On the rate of convergence to equilibrium of countable ergodic Markov chains, Prépublication, Università degli Studi di Bologna, 1997.
,[29] Dynamical Zeta functions and correlation functions for intermittent interval maps, Prépublication, Università degli Studi di Bologna, 1997.
,[30] Renewal sequences and intermittency, Prépublication, Università degli Studi di Bologna, 1997.
,[31] Closed orbits in homology classes, Publ. Math. IHES 71 (1990) 5-32. | Numdam | MR | Zbl
and ,[32] Renewal theorems in symbolic dynamics with applications to geodesic flows, non euclidean tesselations and their fractal limits, Acta Math. 163 (1989) 1-55. | MR | Zbl
,[33] Closed geodesics in homology classes on surfaces of variable negative curvature, Duke Math. J. 58 (1989) 795-821. | MR | Zbl
,[34] 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. | MR | Zbl
,[35] Kleinian Groups, Springer, Berlin, 1988. | Zbl
,[36] Applications of ergodic theory for the investigation of manifolds of negative curvature, Func. Anal. Appl. 3 (1969) 335-336. | MR | Zbl
,[37] 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. | MR | Zbl
,[38] The resolvant of the Laplacian on locally symmetric spaces, J. Differential Geom. 36 (1992) 663-698. | MR | Zbl
and ,[39] 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. | MR | Zbl
,[40] The limit set of a Fuchsian group, Acta Math. 136 (1976) 241-273. | MR | Zbl
,[41] Homology and closed geodesics in a compact negatively curved surface, Amer. J. Math. 113 (1991) 379-385. | MR | Zbl
,[42] Zeta functions and the periodic orbit structure of hyperbolic dynamics, Astérisque 187-188, Soc. Math. France, 1990. | Numdam | MR | Zbl
and ,[43] Geodesics in homology classes, Duke Math. J. 55 (1987) 287-297. | MR | Zbl
and ,[44] Maps of intervals with indifferent fixed points : thermodynamic formalism and phase transitions, J. Stat. Phys. 66 (1992) 503-514. | MR | Zbl
and ,[45] Foundations of Hyperbolic Geometry, Springer, New York, 1994.
,[46] Sur la théorie ergodique des groupes discrets en géométrie hyperbolique, Thèse de doctorat de l'Université Paris XI, 1999.
,[47] Un théorème de la limite locale pour une classe de fonctions dilatantes et monotones par morceaux, Ann. Probab. 11 (1983) 772-788. | MR | Zbl
,[48] Analyse Réelle et Complexe, Masson, Paris, 1975. | MR | Zbl
,[49] Intermittency and regularized Fredholm determinants, Invent. Math. 135 (1999) 1-24. | MR | Zbl
,[50] Harmonic analysis and discontinuous groups in weakly symmetric spaces with applications to Dirichlet series, J. Indian Math. Soc. 20 (1956) 47-87. | MR | Zbl
,[51] The modular surface and continued fractions, J. London Math. Soc. 31 (1985) 69-80. | MR | Zbl
,[52] Closed orbits in homology classes for Anosov flows, Ergodic Theory Dynamical Systems 13 (1993) 387-408. | MR | Zbl
,[53] Principles of Random Walks, Van Nostrand, Princeton, 1964. | MR | Zbl
,[54] The density at infinity of a discrete group of hyperbolic isometries, Publ. Math. IHES 50 (1979) 171-209. | Numdam | MR | Zbl
,[55] Entropy, Hausdorff measure old and new, and limit sets of geometrically finite Kleinian groups, Acta Math. 153 (1984) 259-277. | MR | Zbl
,[56] Recurrence times and rates of mixing, à paraître, Israel J. Math. (1999). | MR | Zbl
,[57] Trace formula for compact Γ\PSL2(R) and the equidistribution theory of closed geodesics, Duke Math. J. 59 (1989) 27-81. | MR | Zbl
,Cited by Sources: