{"paper":{"title":"On the adjacency quantization in the equation modelling the Josephson effect","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.DS","authors_text":"Alexey Glutsyuk, Dmitry Filimonov, Ilya Schurov, Victor Kleptsyn","submitted_at":"2013-01-30T08:21:12Z","abstract_excerpt":"We investigate two-parametric family of non-autonomous ordinary differential equations on the two-torus $$\\dot x=\\frac{dx}{dt}=\\nu\\sin x + a + s \\sin t, \\ a,\\nu,s\\in\\rr; \\ \\nu\\neq0 \\text {is fixed},$$ that model the Josephson effect from superconductivity. We study its rotation number as a function of parameters $(a,s)$ and its {\\it Arnold tongues}: the level sets of the rotation number that have non-empty interior. Its Arnold tongues have many non-typical properties: they exist only for integer rotation numbers (V.M.Buchstaber, O.V.Karpov, S.I.Tertychnyi (2010); Yu.S.Ilyashenko, D.A.Ryzhov, D"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.7159","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"}