{"paper":{"title":"A Family of Totally Rank One Two-sided Shift Maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Diquan Li, Dongmei Li, Yue Wu, Yunjian Wang","submitted_at":"2016-04-09T19:19:02Z","abstract_excerpt":"'Generalized del Junco-Rudolph's map', a sub-family of generalized Chacon's map (\\cite{FER1}), is introduced. A skew product related to the structure of the Generalized del Junco-Rudolph's map is introduced. A Relative Prime Relation, $h_{k+1}\\equiv 1 \\mod q$ is verified, based on the proposition of iterations of this skew product. We say a measure-preserving transformation $T$ is totally rank one if $T^{q}$ is rank one for every $q\\in \\mathbb{N}$. In this paper, we show that of every Generalized del Junco-Rudolph's map is totally rank one."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.02597","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"}