Determination of all rational preperiodic points for morphisms of PN
Determination of all rational preperiodic points for morphisms of PN
复制标题
确定 PN 态射的所有有理周期前点
DOI：
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发表时间：
2012
影响因子：
2
通讯作者：
Benjamin Hutz
中科院分区：
文献类型：
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作者：
Benjamin Hutz
对于态射$f：¶^N o ^N$，其前向轨道被f$限定的点称为f$的前周期点。本文提出了一个算法，以有效地确定所有的有理预周期点的$f$定义在一个给定的数域$K$。该算法在开源软件Sage中实现，价格为$Q$。此外，一个dynatomic零圈的概念被推广到preperiodic点。沿着检查它们的基本性质，这些广义动力学循环被证明是有效的。
For a morphism $f:¶^N o ¶^N$, the points whose forward orbit by $f$ is finite are called preperiodic points for $f$. This article presents an algorithm to effectively determine all the rational preperiodic points for $f$ defined over a given number field $K$. This algorithm is implemented in the open-source software Sage for $Q$. Additionally, the notion of a dynatomic zero-cycle is generalized to preperiodic points. Along with examining their basic properties, these generalized dynatomic cycles are shown to be effective.