On the criterion of resonance overlap and deformation of separatrices

For two-dimensional images which preserve a surface, a method is indicated for building the skeleton of the separatrix which does not use the smallness of nonlinearity. It is shown in an example of a standard image that near the boundary of global stochasticity the deformation of the separatrix is comparable with the width of the stochastic layer and is substantive in the criterion of resonance overlap. A two resonance model, for which an above stochasticity threshold evaluation is acquired which is in agreement with the results of computer experiments, is also examined.