Anosov representations were introduced by Labourie and Guichard-Wienhard. They aim to be a higher rank generalization of convex cocompact groups of isometries of hyperbolic space. With Kapovich and Leeb we take the point of view of groups acting on the symmetric space.
I plan to start reviewing some basic notions of convex cocompact groups of isometries in hyperbolic space, in particular the different characterizations in terms of quasi-isometries, or on the dynamics of the action on the ideal boundary. Then I shall explain corresponding characterizations for higer rank symmetric spaces of non compact type. This takes into account the rich geometry of symmetric spaces and their ideal boundary; I aim to focus in the coarse geometry aspects and the compactification of the action. One of the key tools is a generalization of Morse lemma in hyperbolic geometry to higer rank symmetric spaces. This generalization involves the use of Finsler geometry, that also plays a role in the compactification