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We establish the global existence and stability to the future of non-linearperturbation of de Sitter-like solutions to the Einstein-Yang-Mills system in$n \geq 4$ spacetime dimension. This generalizes Friedrich'sEinstein-Yang-Mills stability results in dimension $n=4$ [ J Differ Geom 34(1991), 275-345] to all higher dimensions.

Future global existence and stability of de Sitter-like solutions to the Einstein-Yang-Mills equations in spacetime dimensions $n\geq 4$