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Roughly speaking, an attractor is an invariant set which attracts everything in a neighborhood of itself. Attractors persist in the sense that, given a system with an attractor, every nearby system has a corresponding attractor. As before, one can ask how big a perturbation is allowed.

As described in detail , the answer is intimately tied to the strength by which the attractor attracts. Strong attractors persist further than weak attractors. An attractor will persist for all systems within a distance, in the metric, given by the intensity of attraction.

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