A study on differences in properties of the logistic maps over integers affected by rounding

On the studies of the logistic map, many reports are presented because of the simple structure of the equation. Calculations with finite precision are usually used for implementations of the map for computers. Then a rounding is needed to these calculations. There are five major methods to implement rounding, but there was not any paper on the rounding of the map. In the present paper, we get some experimental results that the properties of sequences change greatly by roundings, and give some theoretical analyses of them. Then we will give principal reasons that the map with a floor function for rounding generates long aperiodic subsequences.