{"paper":{"title":"Locally connected models for Julia sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GN"],"primary_cat":"math.DS","authors_text":"A. Blokh, C. Curry, L. Oversteegen","submitted_at":"2008-09-22T17:54:24Z","abstract_excerpt":"Let $P$ be a polynomial with a connected Julia set $J$. We use continuum theory to show that it admits a \\emph{finest monotone map $\\ph$ onto a locally connected continuum $J_{\\sim_P}$}, i.e. a monotone map $\\ph:J\\to J_{\\sim_P}$ such that for any other monotone map $\\psi:J\\to J'$ there exists a monotone map $h$ with $\\psi=h\\circ \\ph$. Then we extend $\\ph$ onto the complex plane $\\C$ (keeping the same notation) and show that $\\ph$ monotonically semiconjugates $P|_{\\C}$ to a \\emph{topological polynomial $g:\\C\\to \\C$}. If $P$ does not have Siegel or Cremer periodic points this gives an alternativ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0809.3754","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"}