Sur les processus quasi-Markoviens et certains de leurs facteurs
Tom 103 / 2005
Colloquium Mathematicum 103 (2005), 215-230 MSC: Primary 37A35. DOI: 10.4064/cm103-2-7
We study a class of stationary finite state processes, called quasi-Markovian, including in particular the processes whose law is a Gibbs measure as defined by Bowen. We show that, if a factor with integrable coding time of a quasi-Markovian process is maximal in entropy, then this factor splits off, which means that it admits a Bernoulli shift as an independent complement. If it is not maximal in entropy, then we can find a splitting finite extension of this factor, which generalizes a theorem of Rahe. In particular, this result applies to a factor of a hyperbolic automorphism of the torus generated by a partition which is regular enough.