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 .
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 .
@article{AIF_2015__65_3_1005_0,
author = {Nie, Xin},
title = {On the Hilbert geometry of simplicial Tits sets},
journal = {Annales de l'Institut Fourier},
volume = {65},
year = {2015},
pages = {1005-1030},
doi = {10.5802/aif.2950},
language = {en},
url = {http://dml.mathdoc.fr/item/AIF_2015__65_3_1005_0}
}
Nie, Xin. On the Hilbert geometry of simplicial Tits sets. Annales de l'Institut Fourier, Tome 65 (2015) pp. 1005-1030. doi : 10.5802/aif.2950. http://gdmltest.u-ga.fr/item/AIF_2015__65_3_1005_0/
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