论文标题
同时合理的第二学位合理图
Simultaneous Rational Periodic Points of Degree-2 Rational Maps
论文作者
论文摘要
令$ s $是二次多项式地图的集合，并且学位$ 2 $ - 理性的地图，其自动形态组是同构为$ C_2 $在有理领域定义的。假设Poonen和Manes的标准猜想是在$ S $中的地图下的周期点的周期性长度上的标准猜想，我们对Triples $（F_1，F_2，P）$的完整描述，使得$ P $是S $，$ i = 1,2 $的$ f_i \的合理定期。我们还表明，在理性场上，不超过三个二次多项式图可以具有共同的周期点。此外，在这些假设下，我们表明两个非零有理数$ a，b $是地图的周期点$ ϕ_ {t_1，t_1，t_2}（z）= t_1 z + t_2/z $，用于无限的许多非零合理对$（t_1，t_1，t_2）$，并且仅在$ a^2 = b^b^b^b^b^b^b^b^b^b^b^b^2 $（t_1，t_2）$中。
Let $S$ be the collection of quadratic polynomial maps, and degree $2$-rational maps whose automorphism groups are isomorphic to $C_2$ 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 $(f_1,f_2,p)$ such that $p$ is a rational periodic point for both $f_i\in S$, $i=1,2$. 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 $ϕ_{t_1,t_2}(z)=t_1 z + t_2/z$ for infinitely many nonzero rational pairs $(t_1, t_2)$ if and only if $a^2 = b^2$.
