Entropy and extended memory in discrete chaotic dynamics

We investigate simple one-dimensional maps which allow for exact solutions of their related statistical properties. In addition to the originally refined dynamical description a coarse-grained level of description based on certain partitions of the phase space is selected. The deterministic micropscopic dynamics is shifted to a stochastic symbolic dynamics. The higher order entropies are studied for the logistic map, the tent map, and the shark fin map. Markov sources of any prescribed order are constructed explicitly. In a special case, long memory tails are observed. Systems of this type may be of interest for modelling naturally ocurring phenomena.