P-adic and adelic rational dynamical systems

Abstract

In the framework of adelic approach we consider real and p-adic properties of dynamical system given by linear fractional map f(x) = (a x + b)/(cx + d), where a, b, c, and d are rational numbers. In particular, we investigate behavior of this adelic dynamical system when fixed points are rational. It is shown that any of rational fixed points is p-adic indifferent for all but a finite set of primes. Only for finite number of p-adic cases a rational fixed point may be attractive or repelling. The present analysis is a continuation of the paper math-ph/0612058. Some possible generalizations are discussed.