Splitting of separatrices and symbolic dynamics for some degenerate standard-like maps (Q1803759)

The author deals with standard-like continuously differentiable maps with parabolic fixed points whose second derivatives have jump discontinuities at the fixed points. An asymptotic formula for the splitting of the separatrices is obtained. The structure of a certain chaotic set in the stochastic layer around the separatrices is described in terms of symbolic dynamics. In particular, it is shown that swinging and rotating regimes of motion may alternate in time arbitrarily.