. Finally, then d(?(s), ?(t)) grows at least as in the Euclidean case according to the formula (16), hence the rays are not Busemann equivalent

T. Anderson and R. Schoen, Positive Harmonic Functions on Complete Manifolds of Negative Curvature, The Annals of Mathematics, vol.121, issue.2, pp.429-461, 1985.
DOI : 10.2307/1971181

B. N. Apanasov, Geometrically finite groups of transformations of space, Siberian Math, Journal, vol.23, issue.6, pp.771-780, 1982.

W. Ballmann, Lectures on spaces of nonpositive curvature. With an appendix by Misha Brin, DMV Seminar, 1995.

W. Ballmann, M. Gromov, and V. Schroeder, Manifolds of non positive curvature, Progress in Math. 61 Birkhäuser, 1985.
DOI : 10.1007/BF02565638

I. Belegradek and V. Kapovitch, Classification of negatively pinched manifolds with amenable fundamental groups, Acta Math, pp.229-260, 2006.

M. Bjorklund, Central Limit Theorems for Gromov Hyperbolic Groups, Journal of Theoretical Probability, vol.302, issue.1
DOI : 10.1007/s10959-009-0230-x

M. Bourdon, Structure conforme au bord et flot géodésique dun CAT(?1)-espace, Enseign. Math, issue.2, pp.41-63, 1995.

B. H. Bowditch, Geometrical finiteness with variable negative curvature, Duke Math, J. vol, vol.77, pp.229-274, 1995.

B. H. Bowditch, Discrete parabolic groups, Journal of Differential Geometry, vol.38, issue.3, pp.559-583, 1993.
DOI : 10.4310/jdg/1214454483

URL : http://projecteuclid.org/download/pdf_1/euclid.jdg/1214454483

M. R. Bridson and A. Haefliger, Metric Spaces of Non-Positive Curvature, Grundlehren der Mathematischen Wissenschaften, vol.319, 1999.
DOI : 10.1007/978-3-662-12494-9

H. Busemann, The geometry of geodesics, 1955.

F. Dal-'bo, Trajectoires géodésiques et horocycliques, EDP Science/CNRS Editions, 2007.

F. Dal-'bo and A. N. Starkov, On a classification of limit points of infinitely generated Schottky groups, Journal of Dynamical and Control Systems, vol.6, issue.4, pp.561-578, 2000.
DOI : 10.1023/A:1009556612040

P. Eberlein, Geometry of nonpositively curved manifolds, Chicago Lectures in Mathematics

P. Eberlein and B. Neill, Visibility manifolds, Pac, J. Math, vol.46, pp.45-110, 1973.
DOI : 10.2140/pjm.1973.46.45

A. Fathi, F. Laudenbach, and V. Poénaru, Travaux de Thurston sur les surfaces, Astérisque 66-67, Soc. Math. Fr, 1979.

M. Gromov, Hyperbolic manifolds, groups and actions, in Riemann surfaces and related topics: Proceedings of the 1978 Stony Brook Conference 182-213, 1981.

Y. Guivarc-'h, L. Ji, and J. C. Taylor, Compactifications of symmetric spaces, Progress in Math, 1998.

A. Haas, Dirichlet points, Garnett points, and infinite ends of hyperbolic surfaces. I Ann, Acad. Sci. Fenn. Math, vol.21, issue.1, pp.3-29, 1996.

J. Hadamard, Les surfacesàsurfaces`surfacesà courbures opposées et leurs lignes géodésiques, Journal de mathématiques pures et appliquées 5e série, pp.27-74, 1898.

N. Innami, On the terminal points of co-rays and rays, Archiv der Mathematik, vol.9, issue.5, pp.468-470, 1985.
DOI : 10.1007/BF01195373

L. Ji and R. Macpherson, Geometry of compactifications of locally symmetric spaces, Ann. Institut Fourier 52 no, pp.457-559, 2002.

M. J. Jeon and T. S. Kim, Points at infinity of complete open Riemannian manifolds, J. Korea Soc. Mat. Educ. Ser. B: Pure Appl. Math, vol.11, issue.4, pp.309-321, 2004.

T. Klein and A. Nicas, The horofunction boundary of the Heisenberg group, Pacific Journal of Mathematics, vol.242, issue.2, pp.299-310, 2009.
DOI : 10.2140/pjm.2009.242.299

F. Ledrappier and X. Wang, An integral formula for the volume entropy with applications to rigidity, Journal of Differential Geometry, vol.85, issue.3, p.370, 2009.
DOI : 10.4310/jdg/1292940691

G. M. Lewis, Cut loci of points at infinity, Pacific Journal of Mathematics, vol.43, issue.3, pp.675-690, 1972.
DOI : 10.2140/pjm.1972.43.675

J. D. Mccarthy and A. Papadopoulos, The visual sphere of Teichmüller space and a theorem of Masur-Wolf, Ann. Acad. Sci. Fenn. Math, vol.24, issue.1, pp.147-154, 1999.

S. Morosawa, Limit points for infinitely generated Fuchsian groups, Proc. Camb, pp.539-545, 1988.
DOI : 10.1215/S0012-7094-80-04728-6

Y. Nasu, On asymptotic conjugate points, Tohoku Mathematical Journal, vol.7, issue.3, pp.157-165, 1955.
DOI : 10.2748/tmj/1178245053

URL : http://projecteuclid.org/download/pdf_1/euclid.tmj/1178245053

P. J. Nicholls, Garnett Points for Fuchsian Groups, Bulletin of the London Mathematical Society, vol.12, issue.3, pp.216-218, 1980.
DOI : 10.1112/blms/12.3.216

P. J. Nicholls, Ford and Dirichlet regions for discrete groups of hyperbolic motions, Transactions of the American Mathematical Society, vol.282, issue.1, pp.355-365, 1984.
DOI : 10.1090/S0002-9947-1984-0728717-5

P. J. Nicholls and P. L. Waterman, The boundary of convex fundamental domains of Fuchsian groups, Annales Academiae Scientiarum Fennicae Series A I Mathematica, vol.15, issue.1, pp.11-25, 1990.
DOI : 10.5186/aasfm.1990.15

P. J. Nicholls and P. L. Waterman, Limit points via Schottky pairings, Discrete Groups and Geometry, Soc. Lecture Note Ser, vol.173, pp.190-195, 1991.

A. Papadopoulos, Metric Spaces, convexity and nonpositive curvature, Irma Lectures In Mathematics and Theoretical Physics, vol.6, 2005.
DOI : 10.4171/010

URL : https://hal.archives-ouvertes.fr/hal-00943832

K. Shiohama, Topology of complete noncompact manifolds, Geometry of Geodesics and Related Topics, Adv. Studies in Pure Math, vol.3, pp.423-450, 1984.

T. Shioya, The ideal boundaries of complete open surfaces, Tohoku Mathematical Journal, vol.43, issue.1, pp.37-59, 1991.
DOI : 10.2748/tmj/1178227534

A. N. Starkov, Fuchsian groups from the dynamical viewpoint, Journal of Dynamical and Control Systems, vol.97, issue.3, pp.427-445, 1995.
DOI : 10.1007/BF02269378

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.171-202, 1979.
DOI : 10.1007/BF02684773

W. P. Thurston, Three-Dimensional Geometry and Topology, 1997.

C. Walsh, The horofunction boundary of the Hilbert geometry, Advances in Geometry, vol.8, issue.4, pp.503-529, 2008.
DOI : 10.1515/ADVGEOM.2008.032

URL : https://hal.archives-ouvertes.fr/hal-00782827

C. Walsh, The horofunction boundary of finite-dimensional normed spaces, Mathematical Proceedings of the Cambridge Philosophical Society, vol.142, issue.03, pp.497-507, 2007.
DOI : 10.1017/S0305004107000096

C. Webster and A. Winchester, Busemann points of infinite graphs, Transactions of the American Mathematical Society, vol.358, issue.09, pp.4209-4224, 2006.
DOI : 10.1090/S0002-9947-06-03877-3

J. Yim, Convexity of the ideal boundary for complete open surfaces, Transactions of the American Mathematical Society, vol.347, issue.2, pp.687-700, 1995.
DOI : 10.1090/S0002-9947-1995-1243176-1