{"paper":{"title":"Multidimensional contracted rotations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Benito Pires, Jose Pedro Gaivao","submitted_at":"2025-09-22T11:45:12Z","abstract_excerpt":"We study the dynamics of multidimensional contracted rotations and address a problem posed by Y. Bugeaud and J-P. Conze in \\textit{Acta Arithmetica} in 1999. More precisely, we show that if $A$ is an invertible linear contraction of $\\mathbb{R}^d$, then the map $f: [0,1)^d\\to [0,1)^d$ defined by $f(x) = Ax +b\\,\\,(\\textrm{mod}\\,\\mathbb{Z}^d)$ is asymptotically periodic for Lebesgue almost all $b\\in\\mathbb{R}^d$. We also include an example of a family of multidimensional contracted rotations $(d>1)$ not conjugate to the product of one-dimensional contracted rotations $(d=1)$, showing that our re"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.17639","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2509.17639/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"}