Determination of all rational preperiodic points for morphisms of PN
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Abstract:
For a morphism $f:\mathbb {P}^N \to \mathbb {P}^N$, 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 $\mathbb {Q}$. 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.References
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Additional Information
- Benjamin Hutz
- Affiliation: Department of Mathematical Sciences, Florida Institute of Technology, 150 W. University Boulevard, Melbourne, Florida 32901
- Email: bhutz@fit.edu
- Received by editor(s): November 8, 2012
- Received by editor(s) in revised form: April 18, 2013
- Published electronically: May 5, 2014
- © Copyright 2014
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Math. Comp. 84 (2015), 289-308
- MSC (2010): Primary 37P05, 37P15; Secondary 37P45, 37-04
- DOI: https://doi.org/10.1090/S0025-5718-2014-02850-0
- MathSciNet review: 3266961