Relatively dominated representations

Anosov representations give a higher-rank analogue of convex cocompactness in rank-one Lie group which shares many its good geometric and dynamical properties; finiteness rank one may be seen as controlled weakening to allow for isolated failures hyperbolicity. We introduce relatively dominated relativization representations, or other words finiteness. prove that groups admitting must hyperbolic, these induce limit maps with properties, provide examples, draw connections work Kapovich–Leeb also introduces analogues