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We show that robustly transitive endomorphisms of a closed manifolds musthave a non-trivial dominated splitting or be a local diffeomorphism. Thisallows to get some topological obstructions for the existence of robustlytransitive endomorphisms. To obtain the result we must understand the structureof the kernel of the differential and the recurrence to the critical set of theendomorphism after perturbation.

Robust transitivity and domination for endomorphisms displaying critical points