{"paper":{"title":"Uniform bounds for diffeomorphisms of the torus and a conjecture of P. Boyland","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Salvador Addas-Zanata","submitted_at":"2014-03-28T20:15:07Z","abstract_excerpt":"We consider $C^{1+\\epsilon}$ diffeomorphisms of the torus, denoted $f,$ homotopic to the identity and whose rotation sets have interior. We give some uniform bounds on the displacement of points in the plane under iterates of a lift of $f,$ relative to vectors in the boundary of the rotation set and we use these estimates in order to prove that if such a diffeomorphism $f$ preserves area, then the rotation vector of the area measure is an interior point of the rotation set. This settles a strong version of a conjecture proposed by P. Boyland. We also present some new results on the realization"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.7533","kind":"arxiv","version":3},"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"}