Résumé
In this article, we show that some negative curvature may survive when taking the automorphism group of a finitely generated group. More precisely, we prove that the automorphism group Aut(G) of a one-ended hyperbolic group G turns out to be acylindrically hyperbolic. As a consequence, given a group H and a morphism phi: H -> Aut(G), we deduce that the semidirect product G (sic)(phi) is acylindrically hyperbolic if and only if ker(H ->(phi) Aut (G) -> Out (G)) is finite.