Method of Asymptotics beyond All Orders and Restriction on Maps

The method of asymptotics beyond all orders (ABAO) is known to be a useful tool to investigate separatrix splitting of several maps. For a class of simplectic maps, the form of maps is shown to be restricted by the conditions for the ABAO method to work well. More over, we check that the standard map, H' enon map and the cubic map satisfy the restrcitions.