{"paper":{"title":"Skew Products on the Berkovich Projective Line","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AG","math.NT"],"primary_cat":"math.DS","authors_text":"Richard A. P. Birkett","submitted_at":"2023-10-26T17:47:14Z","abstract_excerpt":"In this article, we develop a dynamical theory for what shall be called a skew product on the Berkovich projective line, $\\phi_*: \\mathbb{P}^1_{\\text{an}}(K) \\to \\mathbb{P}^1_{\\text{an}}(K)$ over a non-Archimedean field $K$. These functions are defined algebraically yet strictly generalise the notion of a rational map on $\\mathbb{P}^1_{\\text{an}}$. We describe the analytical, algebraic, and dynamical properties of skew products, including a study of periodic points, and a Fatou/Julia dichotomy. The article culminates with the classification of the connected components of the Fatou set."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2310.17628","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2310.17628/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}