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Abstract: A concept of integration over fractal measures is discussed. We show a possibility to obtain, in some cases, analytical results for such integrals. Furthermore, we discuss two numerical methods (deterministic algorithm and random iterated algorithm), applicable in the general case.
We apply this technique to compute dynamical entropy and generalized dimensions of invariant measures corresponding to iterated function systems (IFSs) with place-dependent probabilities. It is also shown that with certain dynamical systems one can associate the corresponding IFSs in such a way that their generalized entropies are equal. We use this method to compute entropy of some classical and quantum dynamical systems.