Reconnection of Stable/Unstable Manifolds of the Harper Map
  The Harper map is one of the simplest chaotic systems exhibiting reconnection of invariant manifolds. The method of asymptotics beyond all orders (ABAO) is used to construct stable/unstable manifolds of the Harper map. When the parameter changes to the reconnection threshold, the stable/unstable manifolds are shown to acquire new oscillatory portion corresponding to the heteroclinic tangle after the reconnection. 
Shigeru Ajisaka, Shuichi Tasaki