Entropy computing via integration over fractal measures

We discuss the properties of invariant measures corresponding to iterated f unction systems (IFSs) with place-dependent probabilities and compute their Renyi entropies, generalized dimensions, and multifractal spectra. It is s hown that with certain dynamical systems, one can associate the correspondi ng IFSs in such a way that their generalized entropies are equal. This prov ides a new method of computing entropy for some classical and quantum dynam ical systems. Numerical techniques are based on integration over the fracta l measures. (C) 2000 American Institute of Physics. [S1054-1500(99)01204-5] .