GENERALIZED ENTROPIES - RENYI AND CORRELATION INTEGRAL APPROACH

We study the generalized Renyi entropies which were introduced in the physics literature. The proper defintion of these entropies needs, in our opinion, further clarification. We show that the Renyi entropies d o not contain any new information. On the other hand, we introduce the notion of the correlation entropies, which are not invariants of the dynamical systems in the measure-theoretic sense, but they are invaria nt under transformations of the state space with bounded distortion. W ith these correlation entropies we provide a formal definition which c an serve as a basis for the results reported in the physics literature .