Smooth classification of Cartan actions of higher rank semisimple Lie   groups and their lattices
  Let G be a connected semisimple Lie group without compact factors whose real rank is at least 2, and let \Gamma \subset G be an irreducible lattice. We provide a C^\infty classification for volume-preserving Cartan actions of \Gamma and G. Also, if G has real rank at least 3, we provide a C^\infty classification for volume-preserving, multiplicity free, trellised, Anosov actions on compact manifolds. 
Edward R. Goetze, Ralf J. Spatzier