The information cocycle andɛ-bounded codes

We shall prove here that Bowen’s bounded codes lead to a cocycle-coboundary equation which can be exploited in various ways: through central limit theorems, through the related information variance or through a certain group invariant. Another result which emerges is that it is impossible to boundedly code two Markov automorphisms when one is of maximal type and the other is not. The functions which appear in the above cited cocycle-coboundary equation may belong to variousL ^p spaces. We devote a section to this problem. Finally we show that the information cocycle associated with small smooth partitions of aC ² Anosov diffeomorphism preserving a smooth probability is, in a sense, canonical.