PHASE-SHIFT IN EXPERIMENTAL TRAJECTORY SCALING FUNCTIONS

For one-dimensional maps the trajectory scaling function is invariant under coordinate transformations and can be used to compute any ergodi c average. It is the most stringent test between theory and experiment , but so far it has proven difficult to extract from experimental data . It is shown that the main difficulty is a dephasing of the experimen tal orbit which can be corrected by reconstructing the dynamics from s everal time series. From the reconstructed dynamics the scaling functi on can be accurately extracted.