Anosov representations with Lipschitz limit set
Abstract
We study Anosov representations whose limit set has intermediate regularity, namely is a Lipschitz submanifold of a flag manifold. We introduce an explicit linear functional, the unstable Jacobian, whose orbit growth rate is integral on this class of representations. We prove that many interesting higher rank representations, including $\Theta$positive representations, belong to this class, and establish several applications to rigidity results on the orbit growth rate in the symmetric space.
 Publication:

arXiv eprints
 Pub Date:
 October 2019
 arXiv:
 arXiv:1910.06627
 Bibcode:
 2019arXiv191006627P
 Keywords:

 Mathematics  Differential Geometry;
 Mathematics  Dynamical Systems;
 Mathematics  Group Theory
 EPrint:
 several changes in the introduction, minor corrections elsewhere