{"paper":{"title":"Intermediate \\beta-shifts of finite type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.DS","authors_text":"Bing Li, Tony Samuel, Tuomas Sahlsten","submitted_at":"2014-01-27T21:22:25Z","abstract_excerpt":"An aim of this article is to highlight dynamical differences between the greedy, and hence the lazy, $\\beta$-shift (transformation) and an intermediate $\\beta$-shift (transformation), for a fixed $\\beta \\in (1, 2)$. Specifically, a classification in terms of the kneading invariants of the linear maps $T_{\\beta,\\alpha} \\colon x \\mapsto \\beta x + \\alpha \\bmod 1$ for which the corresponding intermediate $\\beta$-shift is of finite type is given. This characterisation is then employed to construct a class of pairs $(\\beta,\\alpha)$ such that the intermediate $\\beta$-shift associated with $T_{\\beta, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.7027","kind":"arxiv","version":3},"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"}