Difficulties in using averaged orbits to extract scaling functions

Trajectory scaling functions are the basic element in the study of chaotic dynamical systems from which any long-time average can be computed. They have never been extracted from an experimental time series, the reason being their sensitivity to noise. It is shown, by numerical simulations, that the scaling function is more sensitive to drift in the control parameters than to noise in the time series. It is also explained how naive averaging of the orbit points may lead to erroneous results