Authors: Dragović, Branko 
Khrennikov, Andrei
Mihajlović, Dušan
Title: Linear fraction P-Adic and adelic dynamical systems
Journal: Reports on Mathematical Physics
Volume: 60
Issue: 1
First page: 55
Last page: 68
Issue Date: 1-Aug-2007
Rank: M23
ISSN: 0034-4877
DOI: 10.1016/S0034-4877(07)80098-X
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 behaviour 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. Basins of attraction, the Siegel disks and adelic trajectory are examined. It is also shown that real and p-adic norms of any nonzero rational fixed point are connected by adelic product formula.
Keywords: adelic dynamics | fixed points. | p-adic dynamics
Publisher: Elsevier

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