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
.