C. Cuesta and A. Rechtman, Averaging sequences, Pacific Journal of Mathematics, vol.255, issue.1, pp.1-23, 2012.
DOI : 10.2140/pjm.2012.255.1

]. S. Al and . Alvarez, Discretization of harmonic measures for foliated bundles, C. R. Acad. Sci. Paris, Ser I, vol.350, pp.621-626, 2012.

]. D. An and . Anosov, Geodesic flows on closed Riemannian manifolds with negative curvature, Proc. Steklov Math, 1969.

. T. As-]-m, R. Anderson, and . Schoen, Positive harmonic functions on complete manifolds of negative curvature, Ann. of Math, vol.121, pp.429-461, 1985.

D. Anosov and Y. Sinai, SOME SMOOTH ERGODIC SYSTEMS, Russian Mathematical Surveys, vol.22, issue.5, pp.103-167, 1967.
DOI : 10.1070/RM1967v022n05ABEH001228

M. Babillot and F. Ledrappier, Geodesic paths and horocycle flows on abelian covers, Lie Groups and ergodic theory, Tata Inst. Fund. Res. Stud. Math, pp.14-15, 1996.

W. Ballmann, Lectures on Spaces of Nonpositive Curvature, 1995.
DOI : 10.1007/978-3-0348-9240-7

W. Ballmann and F. Ledrappier, Discretization of positive harmonic functions on Riemannian manifolds and Martin boundary, Actes de la Table Ronde de la Géométrie Différentielle, Sémin. Congr. Soc. Math. Fr, vol.1, pp.77-92, 1992.

]. L. Be and . Bers, Simultaneous Uniformization, Bull. Amer. Math. Soc, vol.66, pp.94-97, 1960.

C. Bonatti, L. Díaz, and M. Viana, Dynamics Beyond Uniform Hyperbolicity. A global geometric and probabilistic perspective, Encyclopaedia of Mathematical Sciences Mathematical Physics, III, 2005.

. C. Bgv, X. Bonatti, M. Gómez-mont, and . Viana, Généricité d'exposants de Lyapunov non-nuls pour des produits déterministes de matrices, Ann. I. H. Poincaré. Anal. Non Lin, vol.20, pp.579-624, 2003.

C. Bonatti, X. Gómez-mont, and R. Vila, Statistical behaviour of the leaves of Riccati foliations, Ergodic Theory and Dynamical Systems, vol.27, issue.01, pp.67-96, 2010.
DOI : 10.1017/S0143385708001028

. C. Bv, M. Bonatti, and . Viana, Lyapunov exponents with multiplicity 1 for deterministic products of matrices, Ergod. Th. & Dynam. Sys, vol.24, pp.1295-1330, 2004.

R. Bowen, Symbolic Dynamics for Hyperbolic Flows, American Journal of Mathematics, vol.95, issue.2, pp.429-459, 1973.
DOI : 10.2307/2373793
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.667.1357

]. R. Bo2 and . Bowen, Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms, Lecture Notes in Math, vol.470, 1975.

R. Bowen, Hausdorff dimension of quasi-circles, Publications math??matiques de l'IH??S, vol.34, issue.3, pp.259-273, 1979.
DOI : 10.1007/BF02684767

R. Bowen and B. Marcus, Unique ergodicity for horocycle foliations, Israel Journal of Mathematics, vol.18, issue.1, pp.43-67, 1977.
DOI : 10.1007/BF03007655

R. Bowen and D. Ruelle, The ergodic theory of AxiomA flows, Inventiones Mathematicae, vol.73, issue.3, pp.181-202, 1975.
DOI : 10.1007/BF01389848

M. Bridson and A. Haefliger, Metric spaces of non-positive curvature, Grundlehren Math. Wiss, vol.319, 1999.
DOI : 10.1007/978-3-662-12494-9

C. Camacho and A. Neto, Geometric Theory of Foliations, 1985.
DOI : 10.1007/978-1-4612-5292-4

]. A. Ca and . Candel, Uniformization of surface laminations, Ann. Scient. Éc. Norm. Sup, vol.26, pp.483-516, 1993.

]. I. Ch and . Chavel, Eigenvalues in Riemannian Geometry, 1984.

. J. Ce, D. Cheeger, and . Ebin, Comparison Theorems in Riemannian Geometry, 2008.

[. Y. Cheng and S. T. Yau, Differential equations on riemannian manifolds and their geometric applications, Communications on Pure and Applied Mathematics, vol.1, issue.3, pp.333-354, 1975.
DOI : 10.1002/cpa.3160280303

. C. Cm, M. Connell, and . Martínez, Harmonic and invariant measures on foliated spaces, pre- print

. A. Dgm, B. Debiard, E. Gaveau, and . Mazet, Théorèmes de comparaison en géométrie Riemannienne, Publ. RIMS, Kyoto Univ, vol.12, pp.391-425, 1976.

B. Deroin and V. Kleptsyn, Random Conformal Dynamical Systems, Geometric and Functional Analysis, vol.17, issue.4, pp.1043-1105, 2007.
DOI : 10.1007/s00039-007-0606-y
URL : https://hal.archives-ouvertes.fr/hal-00463764

H. Furstenberg, Noncommuting random products, Transactions of the American Mathematical Society, vol.108, issue.3, pp.377-428, 1963.
DOI : 10.1090/S0002-9947-1963-0163345-0

H. Furstenberg, Random walks and discrete subgroups of Lie groups, Adv. Probab. Related Topics, vol.1, pp.1-63, 1971.

L. Garnett, Foliations, the ergodic theorem and Brownian motion, Journal of Functional Analysis, vol.51, issue.3, pp.285-311, 1983.
DOI : 10.1016/0022-1236(83)90015-0

]. E. Gh and . Ghys, Topologie des feuilles génériques, Ann. of Math, vol.141, pp.387-422, 1995.

E. Ghys, R. Langevin, and P. Walczak, Entropie geometrique des feuilletages, Acta Mathematica, vol.160, issue.0, pp.105-142, 1988.
DOI : 10.1007/BF02392274

]. S. Gpl, J. Goodman, and . Plante, Holonomy and averaging in foliated sets, J. Diff. Geo, vol.14, pp.401-407, 1979.

]. M. Gro and . Gromov, Three remarks on geodesic dynamics and fundamental group, L'Enseign, Math, vol.46, pp.391-402, 2000.

A. [. Guivarc-'h and . Raugi, Frontière de Furstenberg, propriété de contraction et théorèmes de convergence, Z. Wahrsch. Verw. Gebiete, pp.69-187, 1985.

U. Hämenstadt, An explicite description of harmonic measure, Ha2] U.Hämenstadt, Cocycles, Hausdorff measures and cross ratios, pp.287-299, 1990.
DOI : 10.1007/BF02571241

E. Heintze and H. Hof, Geometry of horospheres, Journal of Differential Geometry, vol.12, issue.4, pp.481-491, 1977.
DOI : 10.4310/jdg/1214434219

M. Hirsch, C. Pugh, and M. Shub, Invariant manifolds, Lecture Notes in Math, vol.583, 1977.

V. Kaimanovich, Invariant measures of the geodesic flow and measures at infinity on negatively curved manifolds, Ann. I. H. Poincaré. Phys. Théor, vol.53, pp.361-393, 1990.

V. Kaimanovich and . Amenability, Amenability, hyperfiniteness, and isoperimetric inequalities, Comptes Rendus de l'Acad??mie des Sciences - Series I - Mathematics, vol.325, issue.9, pp.999-1004, 1997.
DOI : 10.1016/S0764-4442(97)89093-3

. [. Kaimanovich, Discretization of bounded harmonic functions on Riemannian manifolds and entropy, Potential theory, de Gruyter, pp.213-223, 1990.

M. [. Kaimanovich and . Lyubich, Conformal and harmonic measures on laminations associated with rational maps, Mem. Amer, Math. Soc, p.173, 2005.

]. A. Ka1 and . Katok, Entropy and closed geodesics, Ergod. Th. & Dynam. Sys, vol.2, pp.339-365, 1982.

]. A. Ka2 and . Katok, Four applications of conformal equivalence to geometry and dynamics, Ergod . Th. & Dynam. Sys, vol.8, pp.115-140, 1988.

G. Knieper, Spherical means on compact Riemannian manifolds of negative curvature, Differential Geometry and its Applications, vol.4, issue.4, pp.361-390, 1994.
DOI : 10.1016/0926-2245(94)90004-3

R. Langevin and P. Walczak, Entropy, transverse entropy and partitions of unity, Ergodic Theory and Dynamical Systems, vol.1342, issue.03, pp.14-551, 1994.
DOI : 10.1007/BF02392274

F. Ledrappier, Ergodic properties of Brownian motion on covers of compact negatively-curve manifolds, Boletim da Sociedade Brasileira de Matem??tica, vol.18, issue.4, pp.115-140, 1988.
DOI : 10.1007/BF02584822

. [. Ledrappier, Harmonic measures and bowen-margulis measures, Israel Journal of Mathematics, vol.18, issue.3, pp.275-287, 1990.
DOI : 10.1007/BF02773746

F. Ledrappier, Structure au bord des vari??t??s ?? courbure n??gative, S??minaire de th??orie spectrale et g??om??trie, vol.13, pp.93-118, 1994.
DOI : 10.5802/tsg.155
URL : http://archive.numdam.org/article/TSG_1994-1995__13__97_0.pdf

F. Ledrappier, A renewal theorem for the distance in negative curvature, Proc. Symp. Pure Math, pp.351-360, 1995.
DOI : 10.1090/pspum/057/1335481

T. Lyons and D. Sullivan, Function theory, random paths and covering spaces, Journal of Differential Geometry, vol.19, issue.2, pp.299-323, 1984.
DOI : 10.4310/jdg/1214438681
URL : http://projecteuclid.org/download/pdf_1/euclid.jdg/1214438681

]. R. Man and . Mañé, Ergodic theory and differentiable dynamicsMargulis, Certain measures associated with U-flows on compact manifolds, Func. Anal. Appl, vol.4, pp.55-67, 1970.

M. Martínez, Measures on hyperbolic surface laminations, Ergodic Theory and Dynamical Systems, vol.26, issue.03, pp.847-867, 2006.
DOI : 10.1017/S0143385706000058

]. S. Mat and . Matsumoto, The dichotomy of harmonic measures of compact hyperbolic laminations, Tohoku Math. J, vol.64, pp.569-592, 2012.

]. P. Matt and . Mattila, Geometry of sets and measure in Euclidian spaces, Fractals and rectifiability, 1995.

C. Moore and C. Schochet, Global analysis on foliated spaces, Math. Sci. Res. Inst. Publ, vol.9, 2006.

V. Oseledets, A multiplicative ergodic theorem : Lyapunov characteristic numbers for dynamical systems, Trans. Moscow. Math. Soc, vol.19, pp.197-231, 1968.

]. S. Pa and . Patterson, The limit set of a Fuchsian group, Acta Math, vol.136, pp.241-273, 1976.

. Ya, Y. Pesin, and . Sinai, Gibbs measures for partially hyperbolic attractors, Ergod. Th. & Dynam . Sys, vol.2, pp.417-438, 1982.

]. J. Pl1 and . Plante, Anosov flows, Amer. J. of Math, vol.94, pp.729-754, 1971.

J. Plante, Foliations With Measure Preserving Holonomy, The Annals of Mathematics, vol.102, issue.2, pp.327-361, 1975.
DOI : 10.2307/1971034

]. J. Pr and . Prat, Étude asymptotique du mouvement brownien sur une variété riemannienne à courbure négative, C. R. Acad. Sci. Paris, Sér. A-B, vol.272, pp.1586-1589, 1971.

M. Ratner, Markov partitions for anosov flows onn-dimensional manifolds, Israel Journal of Mathematics, vol.73, issue.2, pp.92-114, 1973.
DOI : 10.1007/BF02771776

. [. Roblin, Un Th??or??me de Fatou Pour les Densit??s Conformes Avec Applications Aux Rev??tements Galoisiens en Courbure N??gative, Israel Journal of Mathematics, vol.25, issue.2, pp.333-357, 2005.
DOI : 10.1007/BF02785371

]. V. Ro and . Rokhlin, On the fundamental ideas of measure theory, Amer, Math. Soc. Transl, vol.10, pp.1-52, 1962.

]. W. Ru and . Rudin, Real and complex analysis, 1987.

B. Schapira, Mesures quasi-invariantes pour un feuilletage et limites de moyennes longitudinales, Comptes Rendus Mathematique, vol.336, issue.4, pp.349-352, 2003.
DOI : 10.1016/S1631-073X(03)00038-4

]. M. Sh and . Shub, Stabilité globale des systèmes dynamiques, Astérisque, 1978.

. Ya and . Sinai, Gibbs measures in ergodic theory, Russ. Math. Surveys, vol.27, pp.21-69, 1972.

D. Sullivan, The density at infinity of a discrete group of hyperbolic motions, Publications math??matiques de l'IH??S, vol.132, issue.1, pp.172-202, 1979.
DOI : 10.1007/BF02684773

D. Sullivan, The Dirichlet problem at infinity for a negatively curved manifold, Journal of Differential Geometry, vol.18, issue.4, pp.723-732, 1983.
DOI : 10.4310/jdg/1214438179

. [. Thurston, Geometry and topology of 3-manifolds, Princeton Lecture Notes, 1980, currently available at library.msri.org/books/gt3m

P. Walczak, Dynamics of the geodesic flow of a foliation, Ergodic Theory and Dynamical Systems, vol.2, issue.04, pp.637-650, 1988.
DOI : 10.2307/1971239

. [. Wolpert, Thurston's Riemannian metric for Teichm??ller space, Journal of Differential Geometry, vol.23, issue.2, pp.143-174, 1986.
DOI : 10.4310/jdg/1214440024