On boundary maps of Anosov representations of a surface group to SL(3,R)

We prove that Anosov representations from a surface group to SL(3,R) are uniquely determined by their boundary maps if and only if they do not factor over a completely reducible representation. Furthermore we discuss representations not distinguished by their boundary maps, and we give a lower bound for the number of mapping class orbits of components of the space of Anosov representations.