arXiv subjects

Dusan Mihajlovic

Publications and source records attributed to Dusan Mihajlovic.

2 recordsLinked to original sources

arXiv2007

p-Adic and Adelic Rational Dynamical Systems

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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arXiv2006

Linear Fractional p-Adic and Adelic Dynamical Systems

Using an adelic approach we simultaneously consider real and p-adic aspects of dynamical systems whose states are mapped by linear fractional transformations isomorphic to some subgroups of GL (2, Q), SL (2, Q) and SL (2, Z) groups. In particular, we investigate behavior of these adelic systems when fixed points are rational. It is shown that any of these rational fixed points is p-adic indifferent for all but a finite set of primes. Thus only for finite number of p-adic cases a rational fixed point may be attractive or repelling. It is also shown that real and p-adic norms of any nonzero rational fixed point are connected by adelic product formula.

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