Thurston's asymmetric metrics for Anosov representations

We provide a good dynamical framework allowing to generalize Thurston's asymmetric metric and the associated Finsler norm from Teichm\"uller space to large classes of Anosov representations. In many cases, including the space of Hitchin representations, this gives a (possibly asymmetric) Finsler distance. In some cases we explicitly compute the associated Finsler norm.