Reconnection of Stable/Unstable Manifolds of the Harper Map

Details Reconnection of Stable/Unstable Manifolds of the Harper Map Reconnection of Stable/Unstable Manifolds of the Harper Map

2005-01-24

arxiv.org/abs/nlin/0501042v1

Nonlinear Sciences

Chaotic Dynamics

24 pages, 11 figures

Scientific paper

10.1088/1742-6596/31/1/066

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.

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