Symbolic dynamics of fully developed chaos III. Infinite-memory sequences and phase transitions

A special type of dynamical phase transitions which arises in a particular one-dimensional fully developed chaotic iterated map is studied by means of a symbolic dynamics. Exact analytical expressions for the probabilities of words are found on both sides of the critical value, making it possible to give a statistical description of the critical behaviour at the phase transition in terms of Boltzmann entropies, correlation functions and generalized dimensions.