On the Hilbert geometry of simplicial Tits sets
Annales de l'Institut Fourier, Volume 65 (2015) no. 3, p. 1005-1030

The moduli space of convex projective structures on a simplicial hyperbolic Coxeter orbifold is either a point or the real line. Answering a question of M. Crampon, we prove that in the latter case, when one goes to infinity in the moduli space, the entropy of the Hilbert metric tends to 0.

L’espace des modules de structures projectives convexes sur un orbifold simplicial hyperbolique est soit un point soit la droite réelle. En répondant à une question de M. Crampon, nous prouvons que dans ce dernier cas, quand on tend vers l’infini dans l’espace des modules, l’entropie de la métrique de Hilbert tend vers 0.

DOI : https://doi.org/10.5802/aif.2950
Classification:  20F67,  51F15,  53C60
Keywords: convex projective structure, reflection group, Hilbert geometry, volume entropy
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     author = {Nie, Xin},
     title = {On the Hilbert geometry of simplicial Tits sets},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {65},
     number = {3},
     year = {2015},
     pages = {1005-1030},
     doi = {10.5802/aif.2950},
     language = {en},
     url = {http://www.numdam.org/item/AIF_2015__65_3_1005_0}
}
Nie, Xin. On the Hilbert geometry of simplicial Tits sets. Annales de l'Institut Fourier, Volume 65 (2015) no. 3, pp. 1005-1030. doi : 10.5802/aif.2950. http://www.numdam.org/item/AIF_2015__65_3_1005_0/

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