Exponentially small splitting of separatrices, matching in the complex plane and Borel summation

The authors investigate separatrix splitting in rapidly forced systems, taking the standard map as an example. This effect is exponentially small and rather subtle to compute precisely. In order to do so, they use a technique that has been developed for analysing asymptotics beyond all orders in moving interface problems. They obtain an asymptotic result of Lazutkin et. al. (1989) for the separatrices crossing angle. In addition, using Borel summation, the numerical prefactor of the exponentially small term is related to the asymptotic behaviour of the coefficients of a standard asymptotic expansion.