Extended memory processes generated by simple dynamical systems and scaling behavior of the entropy

We study the memory effects in time series generated by unstable non-chaotic dynamical systems and by non-Markovian stochastic sources. For this purpose we compare the decay rate of the Shanonn conditional entropy and the decay rate of the autocorrelations. These rates are completely distinct owing to the persistence of long range correlations. We obtain scaling behavior for the convergence of the block entropies.