射影空间上二次多项式态射的有理周期点
Rational Periodic Points for Degree Two Polynomial Morphisms on Projective Space
摘要：
本文讨论了射影空间的态射的$\Q$ -有理周期点的存在性。特别是，我们构建了一个无限家庭的态射$¶^N$每个组件是一个度2齐次形式的$N+1$变量，其中有一个$\Q$ -周期点的原始周期$\frac{(N+1)(N+2)}{2} + \lfloor \frac{N-1}{2}\rfloor$。这个结果然后被用来表明，$N$足够大，存在态射的$¶^N$与$\Q$ -合理的周期点的本原周期大于$c(k)N^k$的任何$k$和一些常数$c(k)$。
英文摘要：
This article addresses the existence of $\Q$-rational periodic points for morphisms of projective space. In particular, we construct an infinitely family of morphisms on $¶^N$ where each component is a degree 2 homogeneous form in $N+1$ variables which has a $\Q$-periodic point of primitive period $\frac{(N+1)(N+2)}{2} + \lfloor \frac{N-1}{2}\rfloor$. This result is then used to show that for $N$ large enough there exists morphisms of $¶^N$ with $\Q$-rational periodic points with primitive period larger that $c(k)N^k$ for any $k$ and some constant $c(k)$.
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