This paper is devoted to a first analysis of the class of recurrent AMS formal communication channels. The purpose is to generalize some results and approaches dealing with two-sided channels to a wider class of AMS channels assuming non-invertible shifts and thus to cover, to a certain extent, one-sided channels. The basis is to consider recurrent random processes for which the stationary mean dominates (and not only asymptotically dominates) the AMS probability distribution. Some results established for two-sided channels can be partly extended to recurrent AMS one-sided channels.