{"paper":{"title":"Typical points of univoque sets","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.NT","authors_text":"Derong Kong, Fan L\\\"u","submitted_at":"2015-07-05T06:21:40Z","abstract_excerpt":"Given a positive integer $M$ and a real number $q>1$, we consider the univoque set $\\mathcal{U}_q$ of reals which have a unique $q$-expansion over the alphabet $\\set{0,1,\\cdots,M}$. In this paper we show that for any $x\\in\\mathcal{U}_q$ and all sufficiently small $\\varepsilon>0$ the Hausdorff dimension $\\dim_H\\mathcal{U}_q\\cap(x-\\varepsilon, x+\\varepsilon)$ equals either $\\dim_H\\mathcal{U}_q$ {or} zero.\n  Moreover, we give a complete description of the typical points $x\\in\\mathcal{U}_q$ which satisfy \\[ \\dim_H\\mathcal{U}_q\\cap(x-\\varepsilon, x+\\varepsilon)=\\dim_H\\mathcal{U}_q\\quad\\textrm{for a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.01170","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"}