Geometric structures and Axiom A flows for Anosov subgroups

I'll explain how to associate to any Anosov subgroup a family of non-empty domains of discontinuity in such a way that in the torsion-free case each quotient manifold carries an Axiom A flow. These manifolds possess convenient geometric properties and the Axiom A flows extend Sambarino's refraction flows. In particular, this makes it possible to associate spectra of dynamical resonances to the Anosov subgroup, which was the main goal of my SPP project. This is joint work with Daniel Monclair and Andrew Sanders.