{"paper":{"title":"Synchronization is full measure for all $\\alpha$-deformations of an infinite class of continued fraction transformations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Cor Kraaikamp, Kariane Calta, Thomas A. Schmidt","submitted_at":"2017-01-17T00:54:40Z","abstract_excerpt":"We study an infinite family of one-parameter deformations, so-called $\\alpha$-continued fractions, of interval maps associated to distinct triangle Fuchsian groups. In general for such one-parameter deformations, the function giving the entropy of the map indexed by $\\alpha$ varies in a way directly related to whether or not the orbits of the endpoints of the map synchronize. For two cases of one-parameter deformations associated to the classical case of the modular group $\\text{PSL}_2(\\mathbb Z)$, the set of $\\alpha$ for which synchronization occurs has been determined.\n  Here, we explicitly "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.04498","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"}