{"paper":{"title":"Intersections of multiplicative translates of $3$-adic Cantor sets II: two infinite families","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.MG"],"primary_cat":"math.NT","authors_text":"Artem Bolshakov, Jeffrey C. Lagarias, William C. Abram","submitted_at":"2015-08-24T20:40:41Z","abstract_excerpt":"This paper continues the study of the structure of finite intersections of general multiplicative translates $\\mathcal{C}(M_1,\\ldots,M_n)=\\frac{1}{M_1}\\Sigma_{3,\\bar{2}}\\cap\\cdots\\cap\\frac{1}{M_n}\\Sigma_{3,\\bar{2}}$ for integers $1\\leq M_1<\\cdots<M_n$, where $\\Sigma_{3,\\bar{2}}$ denotes the $3$-adic Cantor set. This study was motivated by questions concerning the discrete dynamical system on the $3$-adic integers $\\mathbb{Z}_3$ given by multiplication by $2$. The exceptional set $\\mathcal{E}(\\mathbb{Z}_3)$ is defined to be the set of all elements of $\\mathbb{Z}_3$ whose forward orbits under th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.05967","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"}