{"paper":{"title":"On the points without universal expansions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG","math.NT"],"primary_cat":"math.DS","authors_text":"Kan Jiang, Karma Dajani","submitted_at":"2017-03-07T01:39:49Z","abstract_excerpt":"Let $1<\\beta<2$. Given any $x\\in[0, (\\beta-1)^{-1}]$, a sequence $(a_n)\\in\\{0,1\\}^{\\mathbb{N}}$ is called a $\\beta$-expansion of $x$ if $x=\\sum_{n=1}^{\\infty}a_n\\beta^{-n}.$ For any $k\\geq 1$ and any $(b_1b_2\\cdots b_k)\\in\\{0,1\\}^{k}$, if there exists some $k_0$ such that $a_{k_0+1}a_{k_0+2}\\cdots a_{k_0+k}=b_1b_2\\cdots b_k$, then we call $(a_n)$ a universal $\\beta$-expansion of $x$.\n  Sidorov \\cite{Sidorov2003}, Dajani and de Vries \\cite{DajaniDeVrie} proved that given any $1<\\beta<2$, then Lebesgue almost every point has uncountably many universal expansions. In this paper we consider the se"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.02172","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"}