{"paper":{"title":"On families of differential equations on two-torus with all phase-lock areas","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Alexey Glutsyuk, Leonid Rybnikov","submitted_at":"2015-05-26T14:49:33Z","abstract_excerpt":"We consider two-parametric families of non-autonomous ordinary differential equations on the two-torus with the coordinates $(x,t)$ of the type $\\dot x=v(x)+A+Bf(t)$. We study its rotation number as a function of the parameters $(A,B)$. The {\\it phase-lock areas} are those level sets of the rotation number function $\\rho=\\rho(A,B)$ that have non-empty interiors. V.M.Buchstaber, O.V.Karpov, S.I.Tertychnyi have studied the case, when $v(x)=\\sin x$ in their joint paper. They have observed the quantization effect: for every smooth periodic function $f(t)$ the family of equations may have phase-loc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.06975","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":""},"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"}