{"paper":{"title":"Bifurcation sets arising from non-integer base expansions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.NT","authors_text":"Derong Kong, Pieter Allaart, Simon Baker","submitted_at":"2017-06-16T09:12:55Z","abstract_excerpt":"Given a positive integer $M$ and $q\\in(1,M+1]$, let $\\mathcal U_q$ be the set of $x\\in[0, M/(q-1)]$ having a unique $q$-expansion: there exists a unique sequence $(x_i)=x_1x_2\\ldots$ with each $x_i\\in\\{0,1,\\ldots, M\\}$ such that\n  \\[\n  x=\\frac{x_1}{q}+\\frac{x_2}{q^2}+\\frac{x_3}{q^3}+\\cdots.\n  \\]\n  Denote by $\\mathbf U_q$ the set of corresponding sequences of all points in $\\mathcal U_q$.\n  It is well-known that the function $H: q\\mapsto h(\\mathbf U_q)$ is a Devil's staircase, where $h(\\mathbf U_q)$ denotes the topological entropy of $\\mathbf U_q$. In this paper we {give several characterizatio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.05190","kind":"arxiv","version":4},"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"}