{"paper":{"title":"Tuning and plateaux for the entropy of $\\alpha$-continued fractions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Carlo Carminati, Giulio Tiozzo","submitted_at":"2011-11-10T18:44:30Z","abstract_excerpt":"The entropy $h(T_\\alpha)$ of $\\alpha$-continued fraction transformations is known to be locally monotone outside a closed, totally disconnected set $\\EE$. We will exploit the explicit description of the fractal structure of $\\EE$ to investigate the self-similarities displayed by the graph of the function $\\alpha \\mapsto h(T_\\alpha)$. Finally, we completely characterize the plateaux occurring in this graph, and classify the local monotonic behaviour."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.2554","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"}