Anosov representations with Lipschitz limit set

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 ,-positive representations, belong to this class, and establish several applications to rigidity results on the orbit growth rate in the symmetric space.