Hausdorff dimension of limit sets for projective Anosov representations
Abstract
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 $\mathbf{P}(\mathbb{R}^{n}) \times \mathbf{P}({\mathbb{R}^{n}}^*)$ is bounded between two critical exponents associated respectively to a highest weight and a simple root.
 Publication:

arXiv eprints
 Pub Date:
 February 2019
 arXiv:
 arXiv:1902.01844
 Bibcode:
 2019arXiv190201844G
 Keywords:

 Mathematics  Differential Geometry;
 Mathematics  Dynamical Systems;
 Mathematics  Geometric Topology