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

The classical theorem of Moser, on the existence of a normal form in the neighbourhood of a hyperbolic equilibrium, is extended to a class of real-analytic Hamiltonians with aperiodically time-dependent perturbations. A stronger result is obtained in the case in which the perturbing function exhibits a time decay.