{"paper":{"title":"Multifractal analysis of the divergence points of Birkhoff averages in $beta$-dynamical systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.DS","authors_text":"Xiaojun Zhao, Yuanhong Chen, Zhenliang Zhang","submitted_at":"2015-12-31T03:10:32Z","abstract_excerpt":"This paper is aimed at a detailed study of the multifractal analysis of the so-called divergence points in the system of $\\beta$-expansions. More precisely, let $([0,1),T_{\\beta})$ be the $\\beta$-dynamical system for a general $\\beta>1$ and $\\psi:[0,1]\\mapsto\\mathbb{R}$ be a continuous function. Denote by $\\textsf{A}(\\psi,x)$ all the accumulation points of $\\Big\\{\\frac{1}{n}\\sum_{j=0}^{n-1}\\psi(T^jx): n\\ge 1\\Big\\}$. The Hausdorff dimensions of the sets $$\\Big\\{x:\\textsf{A}(\\psi,x)\\supset[a,b]\\Big\\},\\ \\ \\Big\\{x:\\textsf{A}(\\psi,x)=[a,b]\\Big\\}, \\ \\Big\\{x:\\textsf{A}(\\psi,x)\\subset[a,b]\\Big\\}$$ i.e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.09205","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"}