W. Ballmann, M. Gromov, and V. Schroeder, Manifolds of nonpositive curvature, Progress in Mathematics. Birkhäuser, vol.61, 1985.
DOI : 10.1007/978-1-4684-9159-3

T. Barthelmé, L. Marquis, and A. Zimmer, Entropy Rigidity of Hilbert and Riemannian Metrics, International Mathematics Research Notices, vol.85, issue.no. 3, 2015.
DOI : 10.1007/s12220-007-9001-z

Y. Benoist and D. Hulin, Cubic differentials and finite volume convex projective surfaces, Geometry & Topology, vol.7, issue.1, pp.595-620, 2013.
DOI : 10.1002/cpa.3160280203

Y. Benoist and D. Hulin, Cubic differentials and hyperbolic convex sets, Journal of Differential Geometry, vol.98, issue.1, pp.1-19, 2014.
DOI : 10.4310/jdg/1406137694

G. Berck, A. Bernig, and C. Vernicos, Volume entropy of Hilbert geometries, Pacific Journal of Mathematics, vol.23, issue.2, pp.201-225, 2010.
DOI : 10.1016/S0926-2245(03)00052-4

URL : https://hal.archives-ouvertes.fr/hal-00819143

R. Bowen, Hausdorff dimension of quasi-circles, Publications math??matiques de l'IH??S, vol.34, issue.3, pp.11-25, 1979.
DOI : 10.1007/BF01403069

E. Calabi, Complete affine hyperspheres I, Symposia Mathematica, pp.19-38, 1971.

. Shiu-yuen, S. Cheng, and . Yau, On the regularity of the Monge-Ampère equation det ? 2 u ?x i ?x j = f (x, u), Communications on Pure and Applied Mathematics, vol.30, issue.1, pp.41-68, 1977.

S. Choi and W. M. Goldman, Convex real projective structures on closed surfaces are closed, Proceedings of the, pp.657-661, 1993.
DOI : 10.1090/S0002-9939-1993-1145415-8

B. Colbois and P. Verovic, Hilbert Geometry for Strictly Convex Domains, Geometriae Dedicata, vol.105, issue.1, pp.29-42, 2004.
DOI : 10.1023/B:GEOM.0000024687.23372.b0

M. Crampon, Entropies of strictly convex projective manifolds, Journal of Modern Dynamics, vol.3, issue.4, pp.511-547, 2009.
DOI : 10.3934/jmd.2009.3.511

URL : https://hal.archives-ouvertes.fr/hal-00375776

M. Crampon and L. Marquis, Geometrical finiteness in Hilbert geometry, Annales de l???institut Fourier, vol.64, issue.6, pp.2299-2377, 2014.
DOI : 10.5802/aif.2914

B. Deroin and N. Tholozan, Dominating Surface Group Representations by Fuchsian Ones, International Mathematics Research Notices, vol.29, issue.1, 2015.
DOI : 10.4310/jdg/1214442885

URL : https://hal.archives-ouvertes.fr/hal-00936075

D. Dumas and M. Wolf, Polynomial cubic differentials and convex polygons in the projective plane. Geometric and Functional Analysis, pp.1734-1798, 2015.

D. Hilbert, Ueber die gerade Linie als k??rzeste Verbindung zweier Punkte, Mathematische Annalen, vol.46, issue.1, pp.91-96
DOI : 10.1007/BF02096204

N. J. Hitchin, Lie groups and Teichmüller space, Topology, issue.3, pp.31449-473, 1992.

L. Keen, COLLARS ON RIEMANN SURFACES, Discontinuous groups and Riemann surfaces (Proc. Conf, pp.263-268, 1973.
DOI : 10.1515/9781400881642-021

F. Labourie, Flat Projective Structures on Surfaces and Cubic Holomorphic Differentials, Pure and Applied Mathematics Quarterly, vol.3, issue.4, 2007.
DOI : 10.4310/PAMQ.2007.v3.n4.a10

URL : http://arxiv.org/pdf/math/0611250v1.pdf

. Gye-seon, T. Lee, and . Zhang, Collar lemma for Hitchin representations, 2014.

C. John and . Loftin, Affine spheres and convex RP n -manifolds, American Journal of Mathematics, vol.123, issue.2, pp.255-274, 2001.

C. John and . Loftin, The compactification of the moduli space of convex RP 2 surfaces, I, Journal of Differential Geometry, vol.68, issue.2, pp.223-276, 2004.

C. John and . Loftin, Flat metrics, cubic differentials and limits of projective holonomies, Geometriae Dedicata, vol.128, issue.1, pp.97-106, 2007.

X. Nie, Entropy degeneration of convex projective surfaces, Conformal Geometry and Dynamics of the American Mathematical Society, vol.19, issue.14, pp.318-322, 2015.
DOI : 10.1090/ecgd/286

URL : http://www.ams.org/ecgd/2015-19-14/S1088-4173-2015-00286-6/S1088-4173-2015-00286-6.pdf

C. Vernicos, Approximability of convex bodies and volume entropy in Hilbert geometry, Pacific Journal of Mathematics, vol.35, issue.1, 2014.
DOI : 10.1090/S0002-9939-2015-12504-X

S. Wolpert, A generalization of the Ahlfors-Schwarz lemma, Proceedings of the American Mathematical Society, vol.84, issue.3, pp.377-378, 1982.
DOI : 10.1090/S0002-9939-1982-0640235-5

T. Zhang, The degeneration of convex RP 2 structures on surfaces, Proceedings of the London Mathematical Society, pp.967-1012, 2015.