Finding periodic points from short time series

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Abstract
We present an algorithm for finding low-order periodic points of chaotic maps from possibly very short time series. No information about the map other than the time series is used. The method finds all the periodic points of a piecewise linear approximation of the map. We present examples showing the effectiveness of the method for the Henon and Ikeda maps and a chaotic electronic circuit, including a “cycle expansion” calculation of the Hausdorff dimension for the Henon map.