@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},
year = {2000},
publisher = {Elsevier},
volume = {4e s{\'e}rie, 33},
number = {1},
doi = {10.1016/s0012-9593(00)00104-x},
mrnumber = {2001b:37043},
zbl = {0984.37033},
language = {fr},
url = {https://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 - https://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 https://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, Série 4, Tome 33 (2000) no. 1, pp. 81-120. doi: 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. | Zbl | MR
[2] , Ein mechanisches System mit quasiergodischen Bahnen, in : Collected Papers, Addison-Wesley, 1965, pp. 499-501.
[3] and , Homology of closed geodesics in a negatively curved manifold, J. Differential Geom. 26 (1987) 81-99. | Zbl | MR
[4] , and , Méthode des opérateurs de transfert : transformations dilatantes de l'intervalle et dénombrement de géodésiques fermées, Soc. Math. France, Astérisque 238, 1996. | Zbl | Numdam | MR
[5] , The exponent of convergence of Poincaré series, Proc. London Math. Soc. 3 (18) (1968) 461-483. | Zbl | MR
[6] and , Zeta functions and transfer operators for piecewise monotone transformations, Comm. Math. Phys. 127 (1990) 459-477. | Zbl | MR
[7] and , Lalley's theorem on periodic orbits of hyperbolic flows, Ergodic Theory Dynamical Systems 18 (1998) 17-39. | Zbl | MR
[8] , The equidistribution of closed geodesics, Amer. J. Math. 94 (1972) 413-423. | Zbl | MR
[9] , Hausdorff dimension of quasi-circles, Publ. Math. IHES 50 (1979). | Zbl | MR | Numdam
[10] and , Closed geodesics in homology classes on hyperbolic manifolds with cusps, C. R. Acad. Sci. Paris Série I 324 (1997) 901-906. | Zbl | MR
[11] , Probability, Addison-Wesley, 1968. | Zbl | MR
[12] , Opérateurs de transfert sur le décalage à alphabet infini et applications, Thèse de l'Université Paris 6, 1996.
[13] and , Markov maps associated with Fuchsian groups, Publ. Math. IHES 50 (1979) 153-170. | Zbl | MR | Numdam
[14] and , Sur les chaines à liaison complètes, Bull. Soc. Math. France 65 (1937) 132-148. | Zbl | JFM | Numdam
[15] , On the bass note of a Schottky group, Acta Math. 160 (1988) 249-284. | Zbl | MR
[16] and , Groupes du ping-pong et géodésiques fermées en courbure -1, Ann. Inst. Fourier 46 (3) (1996) 755-799. | Zbl | MR | Numdam
[17] , and , Stable windings for geodesics under Patterson-Sullivan measure, Prépublication 431 du Laboratoire de Probabilités de l'Université Paris VI, 1998.
[18] and , Statistic of the winding of geodesics on a Riemann surface with finite area and constant negative curvature, Rev. Mat. Iber. 13 (1997) 377-401. | Zbl | MR
[19] , Asymptotics for closed geodesics in a homology class-the finite volume case, Duke Math. J. 55 (1987) 717-757. | Zbl | MR
[20] , Asymptotic singular homology of a complete hyperbolic 3-manifold of finite volume, Proc. London Math. Soc. 79 (1999) 451-480. | Zbl | MR
[21] and , Asymptotic winding of the geodesic flow on modular surfaces and continued fractions, Ann. Sci. ENS 26 (1993) 23-50. | Zbl | MR | Numdam
[22] , Fonctions Zêta de Selberg et surfaces de géométrie finie, Adv. Studies in Pure Math. 21 (1992) 33-72. | Zbl | MR
[23] and , Théorèmes limites pour une classe de chaînes de Markov, et applications aux difféomorphismes d'Anosov, Ann. IHP 24 73-98. | Zbl | MR | Numdam
[24] , Meromorphic extensions of the Zeta function for Axiom A flows, Ergodic Theory Dynamical Systems 10 (1990) 347-360. | Zbl | MR
[25] , The Selberg trace formula and the Riemann Zeta function, Duke Math. J. 43 (1976) 441-482. | Zbl | MR
[26] , Sur un théorème spectral et son application aux noyaux Lipschitziens, Proc. AMS 118 (1993) 637-634. | Zbl | MR
[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. | Zbl | MR
[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] and , Closed orbits in homology classes, Publ. Math. IHES 71 (1990) 5-32. | Zbl | MR | Numdam
[32] , Renewal theorems in symbolic dynamics with applications to geodesic flows, non euclidean tesselations and their fractal limits, Acta Math. 163 (1989) 1-55. | Zbl | MR
[33] , Closed geodesics in homology classes on surfaces of variable negative curvature, Duke Math. J. 58 (1989) 795-821. | Zbl | MR
[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. | Zbl | MR
[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. | Zbl | MR
[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. | Zbl | MR
[38] and , The resolvant of the Laplacian on locally symmetric spaces, J. Differential Geom. 36 (1992) 663-698. | Zbl | MR
[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. | Zbl | MR
[40] , The limit set of a Fuchsian group, Acta Math. 136 (1976) 241-273. | Zbl | MR
[41] , Homology and closed geodesics in a compact negatively curved surface, Amer. J. Math. 113 (1991) 379-385. | Zbl | MR
[42] and , Zeta functions and the periodic orbit structure of hyperbolic dynamics, Astérisque 187-188, Soc. Math. France, 1990. | Zbl | MR | Numdam
[43] and , Geodesics in homology classes, Duke Math. J. 55 (1987) 287-297. | Zbl | MR
[44] and , Maps of intervals with indifferent fixed points : thermodynamic formalism and phase transitions, J. Stat. Phys. 66 (1992) 503-514. | Zbl | MR
[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. | Zbl | MR
[48] , Analyse Réelle et Complexe, Masson, Paris, 1975. | Zbl | MR
[49] , Intermittency and regularized Fredholm determinants, Invent. Math. 135 (1999) 1-24. | Zbl | MR
[50] , Harmonic analysis and discontinuous groups in weakly symmetric spaces with applications to Dirichlet series, J. Indian Math. Soc. 20 (1956) 47-87. | Zbl | MR
[51] , The modular surface and continued fractions, J. London Math. Soc. 31 (1985) 69-80. | Zbl | MR
[52] , Closed orbits in homology classes for Anosov flows, Ergodic Theory Dynamical Systems 13 (1993) 387-408. | Zbl | MR
[53] , Principles of Random Walks, Van Nostrand, Princeton, 1964. | Zbl | MR
[54] , The density at infinity of a discrete group of hyperbolic isometries, Publ. Math. IHES 50 (1979) 171-209. | Zbl | MR | Numdam
[55] , Entropy, Hausdorff measure old and new, and limit sets of geometrically finite Kleinian groups, Acta Math. 153 (1984) 259-277. | Zbl | MR
[56] , Recurrence times and rates of mixing, à paraître, Israel J. Math. (1999). | Zbl | MR
[57] , Trace formula for compact Γ\PSL2(R) and the equidistribution theory of closed geodesics, Duke Math. J. 59 (1989) 27-81. | Zbl | MR
Cité par Sources :






