{"paper":{"title":"On B\\\"{o}ttcher coordinates and quasiregular maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.CV","authors_text":"Alastair Fletcher, Robert Fryer","submitted_at":"2012-05-09T13:29:36Z","abstract_excerpt":"It is well-known that a polynomial f(z)=a_d z^d(1+o(1)) can be conjugated by a holomorphic map phi to w \\mapsto w^d in a neighbourhood of infinity. This map phi is called a B\\\"ottcher coordinate for f near infinity. In this paper we construct a B\\\"ottcher type coordinate for compositions of affine mappings and polynomials, a class of mappings first studied in \"Quasiregular mappings of polynomial type in R^2\" by A.Fletcher and D.Goodman. As an application, we prove that if h is affine and c is a complex number, then h(z)^2+c is not uniformly quasiregular."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.1978","kind":"arxiv","version":1},"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"}