{"paper":{"title":"The rigidity of pseudo-rotations on the two-torus and a question of Norton-Sullivan","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Jian Wang, Zhiyuan Zhang","submitted_at":"2017-08-08T15:43:34Z","abstract_excerpt":"We show that under certain boundedness condition, a $C^{r}$ conservative irrational pseudo-rotations on $\\mathbb{T}^2$ with a generic rotation vector is $C^{r-1}$-rigid. We also obtain $C^0$-rigidity for H\\\"older pseudo-rotations with similar properties. These provide a partial generalisation of the main results in [B. Bramham, Invent. Math. (2015), no. 2, 561-580; A. Avila, B. Fayad, P. Le Calvez, D. Xu and Z. Zhang, arXiv: 1509.06906v1].\n  We then use these results to study conservative irrational pseudo-rotations on $\\mathbb{T}^2$ with a generic rotation vector that is semi-conjugate to a t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.02529","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"}