Splitting of separatrices for standard and semistandard mappings

Abstract

We investigate Chirikov's standard mapping which is a model for the onset of nonintegrability in nonlinear Hamiltonian systems. The asymptotic formula (when the deviation from an integrable system is small) for the angle of intersection of separatrices at a homoclinic point is derived on the basis of approximation by the Green-Percival semistandard mapping in the complex domain. Computed data on the splitting of separatrices for the semi-standard map are presented from which we derive the pre-exponential coefficient in the formula for splitting of separatrices in the standard mapping.