Reconnection of Stable/Unstable Manifolds of the Harper Map
arXiv:nlin/0501042 · doi:10.1088/1742-6596/31/1/066
Abstract
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.
24 pages, 11 figures