{"paper":{"title":"Density of Stable Interval Translation Maps","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Kostiantyn Drach, Leon Staresinic, Sebastian van Strien","submitted_at":"2024-11-21T17:04:29Z","abstract_excerpt":"Assume that the interval $I=[0,1)$ is partitioned into finitely many intervals $I_1,\\dots,I_r$ and consider a map $T\\colon I\\to I$ so that $T_{\\vert I_s}$ is a translation for each $1 \\le s \\le r$. We do not assume that the images of these intervals are disjoint. Such maps are called Interval Translation Maps. Let $ITM(r)$ be the space of all such transformations, where we fix $r$ but not the intervals $I_1,\\dots,I_r$, nor the translations. The set $X(T):=\\bigcap_{n\\ge 0} T^n[0,1)$ can be a finite union of intervals (in which case the map is called of finite type), or is a disjoint union of fi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.14312","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2411.14312/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}