Generalized dimensions and entropies from a measured time series

Abstract
The correlation-integral method of Grassberger and Procaccia is generalized to yield the whole spectrum of dimensions Dq and entropies Kq from a measured time series with a numerical effort which is only insignificantly larger than that needed to determine the original correlation integral. It is shown that our method yields reliable numerical results for the tent map and for the Mackey-Glass equation.