{"paper":{"title":"Rational maps with Fatou components of arbitrarily large connectivity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Jordi Canela","submitted_at":"2017-04-03T12:21:23Z","abstract_excerpt":"We study the family of singular perturbations of Blaschke products $B_{a,\\lambda}(z)=z^3\\frac{z-a}{1-\\overline{a}z}+\\frac{\\lambda}{z^2}$. We analyse how the connectivity of the Fatou components varies as we move continuously the parameter $\\lambda$. We prove that all possible escaping configurations of the critical point $c_-(a,\\lambda)$ take place within the parameter space. In particular, we prove that there are maps $B_{a,\\lambda}$ which have Fatou components of arbitrarily large finite connectivity within their dynamical planes."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.00544","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"}