UNSTABLE PERIODIC ORBIT ANALYSIS OF HISTOGRAMS OF CHAOTIC TIME-SERIES

Using the Lorenz equations, we have investigated whether unstable peri odic orbits (UPOs) associated with a strange attractor may predict the occurrence of the robust sharp peaks in histograms of some experiment al chaotic time series. Histograms with sharp peaks occur for the Lore nz parameter value r = 60.0 but not for r = 28.0, and the sharp peaks for r = 60.0 do not correspond to a histogram derived from any single UFO. However, we show that histograms derived from the time series of a non-Axiom-A chaotic system can be accurately predicted by an escape- time weighting of UFO histograms. [S0031-9007(98)07397-9].