Beyond-All-Orders Asymptotics and Heteroclinic Structures

Abstract

We analyze the chaotic dynamics, by developing the asymptotic expansion beyond all orders exploited for the analysis of separatrices-crossing angle. Choosing the standard map for illustration, we determine the Stokes multiplier (SM) by sharpening the idea on an analytic continuation in crossing the Stokes line. σ-dependent higher-order corrections to the primary (n = 1) SM and the nature of SM for higher-order singularities are revealed. The asymptotic analytical result for the unstable manifold impinging upon a hyperbolic fixed point is shown to reproduce Birkhoff and Smale’s horse-shoe.