{"paper":{"title":"On the bifurcation set of unique expansions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.NT","authors_text":"Charlene Kalle, Derong Kong, Fan L\\\"u, Wenxia Li","submitted_at":"2016-12-23T14:26:41Z","abstract_excerpt":"Given a positive integer $M$, for $q\\in(1, M+1]$ let ${\\mathcal{U}}_q$ be the set of $x\\in[0, M/(q-1)]$ having a unique $q$-expansion with the digit set $\\{0, 1,\\ldots, M\\}$, and let $\\mathbf{U}_q$ be the set of corresponding $q$-expansions. Recently, Komornik et al.~(Adv. Math., 2017) showed that the topological entropy function $H: q \\mapsto h_{top}(\\mathbf{U}_q)$ is a Devil's staircase in $(1, M+1]$. Let $\\mathcal{B}$ be the bifurcation set of $H$ defined by\n  \\[\n  \\mathcal{B}=\\{q\\in(1, M+1]: H(p)\\ne H(q)\\quad\\textrm{for any}\\quad p\\ne q\\}.\n  \\]\n  In this paper we analyze the fractal proper"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.07982","kind":"arxiv","version":5},"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"}