Determination of all rational preperiodic points for morphisms of PN

Abstract

For a morphism $f:{\P }^N\to {\P }^N$, 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.

arXiv comment18 pages. To appear in Mathematics of Computation. Sage implementation of the algorithm is Sage Trac Ticket #14219

References in corpus (1)

• Computing algebraic numbers of bounded height