Cycles and precycles of \(f_{7,2}\) and of \(f_{5,3}\)

In "1 or 2 digits", we saw a figure illustrating the dynamics of the transformation \(f_{2}\), which acts on the two-digits decimal representations between 00 e 99. The following figures show the orbits of the transformations \(f_{7,2}\) and \(f_{5,3}\). In these images, we include the writing of each number in base 10, with the purpose of underlining the dependence of the dynamics with respect to the choice of the base used to represent the number.

Cycles and precycles of \(f_{7,2}\).

Cycles and precycles of \(f_{5,3}\).

You can click on the image to see it in a larger version.