This letter studies a digital return map that is a mapping from a set of lattice points to itself. The digital map can exhibit various periodic orbits. As a typical example, we present the digital logistic map based on the logistic map. Two fundamental results are shown. When the logistic map has a unique periodic orbit, the digital map can have plural periodic orbits. When the logistic map has an unstable period-3 orbit that causes chaos, the digital map can have a stable period-3 orbit with various domain of attractions.