{"paper":{"title":"Fonction complexit\\'e associ\\'ee \\`a une application ergodique du tore","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.DS","authors_text":"Jean-Fran\\c{c}ois Bertazzon","submitted_at":"2012-02-21T09:04:15Z","abstract_excerpt":"In this article we give the optimal lower bound for the complexity function of a planar translation which induces an ergodic rotation of the torus $\\mathbb{R}^2 / \\mathbb{Z}^2$. In addition, we give an explicit calculation of this complexity for the application $(x,y) \\mapsto (x+1/\\phi^2,y+x-1/ (2\\phi^3))$, where $\\phi$ is the golden mean.\n  Nous proposons dans ce travail de minorer de mani\\`ere optimale la fonction complexit\\'e associ\\'ee \\`a une translation du plan, qui induit une rotation ergodique du tore $\\mathbb R^2/\\mathbb Z^2$. De plus, nous donnons un calcul explicite de cette complex"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.4560","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"}