Approximating chaotic time series through unstable periodic orbits

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Abstract
There are many noise reduction methods for chaotic signals, but most only work over a limited signal to noise range. If chaotic signals are to be used for communications, noise reduction techniques which can handle larger amounts of noise (or deterministic noise) are needed. Here I describe a method of approximating a chaotic signal by constructing possible sequences based on unstable periodic orbits. The approximation is good enough to distinguish between chaotic attractors, even when large amounts of noise are added to the chaotic signal.

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