Simultaneous rational periodic points of degree-2 rational maps

Barsakçı, Burcu and Sadek, Mohammad (2023) Simultaneous rational periodic points of degree-2 rational maps. Journal of Number Theory, 243 . pp. 715-728. ISSN 0022-314X (Print) 1096-1658 (Online)

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Let S be the collection of quadratic polynomial maps, and degree 2-rational 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 degree-2
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

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