{"paper":{"title":"Recomposing rational functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV","math.NT"],"primary_cat":"math.DS","authors_text":"Fedor Pakovich","submitted_at":"2016-10-20T13:50:02Z","abstract_excerpt":"Let $A$ be a rational function. For any decomposition of $A$ into a composition of rational functions $A=U\\circ V$ the rational function $\\widetilde A=V\\circ U$ is called an elementary transformation of $A$, and rational functions $A$ and $B$ are called equivalent if there exists a chain of elementary transformations between $A$ and $B$. This equivalence relation naturally appears in the complex dynamics as a part of the problem of describing of semiconjugate rational functions. In this paper we show that for a rational function $A$ its equivalence class $[A]$ contains infinitely many conjugac"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.06411","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":""},"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"}