Papers › Determination of all rational preperiodic points for morphisms of PN
Determination of all rational preperiodic points for morphisms of PN
Benjamin Hutz
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For a morphism f:Pᴺ →Pᴺ, 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.
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