Appears in collection : Homogeneous Dynamics and Geometry in Higher-Rank Lie Groups

The dynamics of a cusped Hitchin representation can be encoded by a locally Holder continuous, eventually positive, non-arithmetic potential with an entropy gap at infinity on a topologically mixing countable Markov shift with the BIP property. After introducing and motivating these notions, I will present an orbit counting theorem for this class of shifts and potentials that, in turn, gives an orbit counting theorem for cusped Hitchin representations. This is joint work with Harry Bray, Dick Canary, and Nyima Kao