{"paper":{"title":"Multiple codings for self-similar sets with overlaps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG","math.NT"],"primary_cat":"math.DS","authors_text":"Derong Kong, Kan Jiang, Karma Dajani, Lifeng Xi, Wenxia Li","submitted_at":"2016-03-30T18:37:17Z","abstract_excerpt":"In this paper we consider a general class $\\mathcal E$ of self-similar sets with complete overlaps. Given a self-similar iterated function system $\\Phi=(E, \\{f_i\\}_{i=1}^m)\\in\\mathcal E$ on the real line, for each point $x\\in E$ we can find a sequence $(i_k)=i_1i_2\\ldots\\in\\{1,\\ldots,m\\}^\\mathbb N$, called a coding of $x$, such that $$ x=\\lim_{n\\to\\infty}f_{i_1}\\circ f_{i_{2}}\\circ\\cdots\\circ f_{i_n}(0). $$ For $k=1,2,\\ldots, \\aleph_0$ or $2^{\\aleph_0}$ we investigate the subset $\\mathcal U_k(\\Phi)$ which consists of all $x\\in E$ having precisely $k$ different codings. Among several equivalent"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.09304","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"}