{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/determination-of-all-rational-preperiodic","title":"Determination of all rational preperiodic points for morphisms of PN","arxiv_id":"1210.6246","date":"2012-10-23","proceeding":null,"authors":["Benjamin Hutz"],"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.","url_abs":"https://arxiv.org/abs/1210.6246v3","url_pdf":"https://arxiv.org/pdf/1210.6246v3.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"determination-of-all-rational-preperiodic","repo_url":"https://github.com/safaama1/Find-all-preperiodic-points-of-Dynamics-System-over-function-fields","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}