Unstable Periodic Orbit Analysis of Histograms of Chaotic Time Series

Using the Lorenz equations, we have investigated whether unstable periodic orbits (UPOs) associated with a strange attractor may predict the occurrence of the robust sharp peaks in histograms of some experimental chaotic time series. Histograms with sharp peaks occur for the Lorenz parameter value r = 60.0 but not for r = 28.0, and the sharp peaks for r = 60.0 do not correspond to any single histogram derived from a UPO. Despite this lack of correspondence, we show that histograms derived from a chaotic time series can be accurately predicted by an escape-time weighting of UPO histograms. 05.45.+b, 05.70.Ln, 82.40.Bj 47.27.Cn, Typeset using REVTEX