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The classical theorem of Moser, on the existence of a normal form in theneighbourhood of a hyperbolic equilibrium, is extended to a class ofreal-analytic Hamiltonians with aperiodically time-dependent perturbations. Astronger result is obtained in the case in which the perturbing functionexhibits a time decay.

Normal forms \`a la Moser for aperiodically time-dependent Hamiltonians in the vicinity of a hyperbolic equilibrium