{"paper":{"title":"The Morse minimal system is nearly continuously Kakutani equivalent to the binary odometer","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Andrew Dykstra, Ayse Sahin","submitted_at":"2014-04-01T14:17:06Z","abstract_excerpt":"Ergodic homeomorphisms $T$ and $S$ of Polish probability spaces $X$ and $Y$ are evenly Kakutani equivalent if there is an orbit equivalence $\\phi: X_0 \\rightarrow Y_0$ between full measure subsets of $X$ and $Y$ such that, for some $A \\subset X_0$ of positive measure, $\\phi$ restricts to a measurable isomorphism of the induced systems $T_A$ and $S_{\\phi(A)}$. The study of even Kakutani equivalence dates back to the seventies, and it is well known that any two zero-entropy loosely Bernoulli systems are evenly Kakutani equivalent. But even Kakutani equivalence is a purely measurable relation, wh"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.0246","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"}