  In our previous investigations, we have developed the renormalization group
method to $p$-adic models on Cayley trees, this method is closely related to
the investigation of $p$-adic dynamical systems associated with a given model.
In this paper, we study chaotic behavior of the Potts-Bethe mapping. We point
out that a similar kind of result is not known in the case of real numbers
(with rigorous proofs).
