Hausdorff Dimension Of Limit Sets For Projective Anosov Representations

Olivier Glorieux (1) , Daniel Monclair (2) , Nicolas Tholozan (3, 4, 5, 6)

1 IHES - Institut des Hautes Études Scientifiques
2 LM-Orsay - Laboratoire de Mathématiques d'Orsay
3 CNRS - Centre National de la Recherche Scientifique
4 DMA - Département de Mathématiques et Applications - ENS Paris
5 PSL - Université Paris Sciences et Lettres
6 Algèbre et Géométrie (DMA)

We study the relation between critical exponents and Haus-dorff dimensions of limit sets for projective Anosov representations. We prove that the Hausdorff dimension of the symmetric limit set in P(R n) × P(R n *) is bounded between two critical exponents associated respectively to a highest weight and a simple root.

Domaines: Mathématiques [math]

Olivier Glorieux, Daniel Monclair, Nicolas Tholozan. Hausdorff Dimension Of Limit Sets For Projective Anosov Representations. 2019. ⟨hal-02419949⟩