Width of stochastic layers in near-integrable two-dimensional symplectic maps. (Q1963445)

The author deals with the width of stochastic layers which are one of the important quantities characterizing chaotic properties of a given analytic symplectic self-map on a two-dimensional domain. The author shows, that under some suitable assumptions the following relation holds: \({w\over d}\sim{1\over \lambda}\), where \(d\) is the width of a lobe domain \(D\) bounded by segments of the separatrices and \(\lambda> 0\) is logarithmic of the larger multiplier at the hyperbolic fixed-point.