p-Adic and Adelic Rational Dynamical Systems
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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)/(c x + 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.
12 pages. Talk at the 4th Summer School in Modern Mathematical Physics, September 2006, Belgrade (Serbia)
12 pages. Talk at the 4th Summer School in Modern Mathematical Physics, September 2006, Belgrade (Serbia)