{"paper":{"title":"An awkward graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Mary Rees","submitted_at":"2018-10-11T13:27:06Z","abstract_excerpt":"Given a rational map $f:\\overline{\\mathbb C}\\to \\overline{\\mathbb C}$ and a finite graph $G\\subset \\overline{\\mathbb C}$ such that $f(G)\\subset G$ and $f$ is expanding on some neighbourhood of $G$, we show that there is another finite graph $G'\\subset \\bigcup _{n\\ge 0}f^{-n}(G)$ in an arbitrarily small neighbourhood of $G$ such that $f^N(G')\\subset G'$ for some integer $N$ but $\\bigcup _{i=0}^{N-1}f^{i}(G')$ contains accumulating {\\em{plaits}} and {\\em{nests}}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.05008","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"}