{"paper":{"title":"Commuting circle diffeomorphisms with their derivatives having mixed moduli of continuity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Enhui Shi, Hui Xu","submitted_at":"2019-04-08T12:09:13Z","abstract_excerpt":"Let $d\\geq 2$ be an integer and let $\\omega_1,\\cdots ,\\omega_d$ be moduli of continuity in a specified class which contains the moduli of H\\\"{o}lder continuity. Let $f_k$, $k\\in\\{1,\\cdots,d\\}$, be $C^{1+\\omega_k}$ orientation preserving diffeomorphisms of the circle and $f_1,\\cdots, f_d$ commute with each other. We prove that if the rotation numbers of $f_k$'s are independent over the rationals and $\\omega_1(t)\\cdots\\omega_d(t)=t\\omega(t)$ with $\\lim_{t\\rightarrow 0^+}\\omega(t)=0$, then $f_1,\\cdots,f_d$ are simultaneously (topologically) conjugate to rigid rotations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.03984","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"}