Formation of a fractal basin boundary in a forced oscillator

The question of how a fractal basin boundary arises in the sinusoidally forced Duffing's equation is considered. The author describes how the backwards system flow deforms a local stable manifold into the fractal boundary. Parts of the boundary are labeled in a way related to their time of formation. The truncated fractal boundary produced by a burst of sinusoidal forcing is briefly considered. The approach supplements the insights provided by the usual Poincare map techniques.<
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