{"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/dynatomic-galois-groups-for-a-family-of","title":"Dynatomic Galois groups for a family of quadratic rational maps","arxiv_id":"2303.05632","date":"2023-03-10","proceeding":null,"authors":["David Krumm","Allan Lacy"],"abstract":"For every nonconstant rational function $\\phi\\in\\mathbb{Q}(x)$, the Galois groups of the dynatomic polynomials of $\\phi$ encode various properties of $\\phi$ that are of interest in the subject of arithmetic dynamics. We study here the structure of these Galois groups as $\\phi$ varies in a particular one-parameter family of maps, namely the quadratic rational maps having a critical point of period 2. In particular, we provide explicit descriptions of the third and fourth dynatomic Galois groups for maps in this family.","url_abs":"https://arxiv.org/abs/2303.05632v3","url_pdf":"https://arxiv.org/pdf/2303.05632v3.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":"dynatomic-galois-groups-for-a-family-of","repo_url":"https://github.com/davidkrumm/dynatomic_groups","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"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}