Barsakçı, Burcu and Sadek, Mohammad (2023) Simultaneous rational periodic points of degree2 rational maps. Journal of Number Theory, 243 . pp. 715728. ISSN 0022314X (Print) 10961658 (Online)
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Official URL: https://dx.doi.org/10.1016/j.jnt.2022.06.005
Abstract
Let S be the collection of quadratic polynomial maps, and degree 2rational maps whose automorphism groups are isomorphic to C2 defined over the rational field. Assuming standard conjectures of Poonen and Manes on the period length of a periodic point under the action of a map in S, we give a complete description of triples (f1,f2,p) such that p is a rational periodic point for both fi∈S, i=1,2. We also show that no more than three quadratic polynomial maps can possess a common periodic point over the rational field. In addition, under these hypotheses we show that two nonzero rational numbers a,b are periodic points of the map ϕt1,t2(z)=t1z+t2/z for infinitely many nonzero rational pairs (t1,t2) if and only if a2=b2.
Item Type:  Article 

Uncontrolled Keywords:  Algebraic curves; Arithmetic dynamics; Periodic points; Quadratic polynomial maps; Rational maps of degree2 
Divisions:  Faculty of Engineering and Natural Sciences 
Depositing User:  Mohammad Sadek 
Date Deposited:  07 Sep 2023 13:39 
Last Modified:  07 Sep 2023 13:39 
URI:  https://research.sabanciuniv.edu/id/eprint/47802 
Available Versions of this Item

Simultaneous rational periodic points of degree2 rational maps. (deposited 19 Aug 2022 23:48)
 Simultaneous rational periodic points of degree2 rational maps. (deposited 07 Sep 2023 13:39) [Currently Displayed]