A study on relations between loops in sequences generated by the logistic map over integers and real numbers

We are interested in properties of the logistic maps with finite precision and theirs sequences. In this paper, we focus on a cyclic part, which we call a loop, in a sequence generated by the logistic map over integers successively, since the loop always exists in the sequence. We can observe loops in sequences generated by the logistic map with irrational numbers as initial values. We will show the relations between loops in sequences generated by the map over integers and real numbers. We will also show a correspondence between these loops by averages of squared differences.