We study the relation between critical exponents and Hausdorff dimensions of limit sets for projective Anosov representations. We prove that the Hausdorff dimension of the symmetric limit set in is bounded between two critical exponents associated respectively to a highest weight and a simple root.
Nous étudions la relation entre les exposants critiques et les dimensions de Hausdorff des ensembles limites pour les représentations projectivement Anosov. Nous prouvons que la dimension de Hausdorff de l’ensemble limite symétrique dans est bornée par deux exposants critiques associés respectivement à un plus haut poids et à une racine simple.
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Keywords: Critical exponent, Hausdorff dimension, Anosov representation, Hilbert geometry
Mot clés : Exposant critique, dimension de Hausdorff, représentation Anosov, géométrie de Hilbert
Olivier Glorieux 1; Daniel Monclair 2; Nicolas Tholozan 3
@article{JEP_2023__10__1157_0, author = {Olivier Glorieux and Daniel Monclair and Nicolas Tholozan}, title = {Hausdorff dimension of limit sets for projective {Anosov} representations}, journal = {Journal de l{\textquoteright}\'Ecole polytechnique {\textemdash} Math\'ematiques}, pages = {1157--1193}, publisher = {\'Ecole polytechnique}, volume = {10}, year = {2023}, doi = {10.5802/jep.241}, language = {en}, url = {https://jep.centre-mersenne.org/articles/10.5802/jep.241/} }
TY - JOUR AU - Olivier Glorieux AU - Daniel Monclair AU - Nicolas Tholozan TI - Hausdorff dimension of limit sets for projective Anosov representations JO - Journal de l’École polytechnique — Mathématiques PY - 2023 SP - 1157 EP - 1193 VL - 10 PB - École polytechnique UR - https://jep.centre-mersenne.org/articles/10.5802/jep.241/ DO - 10.5802/jep.241 LA - en ID - JEP_2023__10__1157_0 ER -
%0 Journal Article %A Olivier Glorieux %A Daniel Monclair %A Nicolas Tholozan %T Hausdorff dimension of limit sets for projective Anosov representations %J Journal de l’École polytechnique — Mathématiques %D 2023 %P 1157-1193 %V 10 %I École polytechnique %U https://jep.centre-mersenne.org/articles/10.5802/jep.241/ %R 10.5802/jep.241 %G en %F JEP_2023__10__1157_0
Olivier Glorieux; Daniel Monclair; Nicolas Tholozan. Hausdorff dimension of limit sets for projective Anosov representations. Journal de l’École polytechnique — Mathématiques, Volume 10 (2023), pp. 1157-1193. doi : 10.5802/jep.241. https://jep.centre-mersenne.org/articles/10.5802/jep.241/
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