An analytic integral along the separatrix of the semistandard map:existence and an exponential estimate for the distance between the stable and unstable separatrices

Неге I give the proof to the existence of separatrices of the semistandard map, the exponential estimate from above for the distance between the stable and unstable separatrices, and the existence of an analytical ingtegral near the unstable separatrix. These three things are necessary for obtaining the asymtotics of separatrices splittings for the standard map with small values of the parameter and for defining quantities entering the asymptotics.