Dynamical integral transform on fractal sets and the computation of entropy

Abstract

We introduce an integral transform of wavelet type, which we call Dynamical Integral Transform, and we show that it can be used to compute the second Renyi entropy for a large class of invariant measures. The method is then generalized to the whole spectrum of the Renyi entropies and establishes a correspondence between thermodynamic formalism and the Dynamical Integral Transform of expanding strange sets. Numerical examples are presented.