{"paper":{"title":"On constrictions of phase-lock areas in model of overdamped Josephson effect and transition matrix of double confluent Heun equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Alexey Glutsyuk","submitted_at":"2018-05-07T17:15:20Z","abstract_excerpt":"We will discuss the model of the overdamped Josephson junction in superconductivity, which is given by a family of first order non-linear ordinary differential equations on two-torus depending on three parameters: a fixed parameter $\\omega$ (the frequency); a pair of variable parameters $(B,A)$ (abscissa and ordinate). It is important to study the rotation number of the system as a function $\\rho=\\rho(B,A)$ and to describe the phase-lock areas: its level sets $L_r=\\{\\rho =r\\}$ with non-empty interiors. They were studied by V.M.Buchstaber, O.V.Karpov, S.I.Tertychnyi, who observed in 2010 that t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.02624","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"}