p-Adic and Adelic Rational Dynamical Systems

Details p-Adic and Adelic Rational Dynamical Systems p-Adic and Adelic Rational Dynamical Systems

2007-07-06

arxiv.org/abs/0707.0984v1

SFIN XX A1 (2007) 187 - 196

Physics

Mathematical Physics

12 pages. Talk at the 4th Summer School in Modern Mathematical Physics, September 2006, Belgrade (Serbia)

Scientific paper

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.

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