{"paper":{"title":"Conjugacies between P-homeomorphisms with several breaks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Akhtam Dzhalilov, Dieter Mayer, Utkir Safarov","submitted_at":"2014-08-25T12:27:00Z","abstract_excerpt":"Let $f_{i},i=1,2$ be orientation preserving circle homeomorphisms with a finite number of break points, at which the first derivatives $Df_{i}$ have jumps, and with identical irrational rotation number $\\rho=\\rho_{f_{1}}=\\rho_{f_{2}}.$ The jump ratio of $f_{i}$ at the break point $b$ is denoted by $\\sigma_{f_{i}}(b)$, i.e. $\\sigma_{f_{i}}(b):=\\frac{Df_{i}(b-0)}{Df_{i}(b+0)}$. Denote by $\\sigma_{f_{i}}, i=1,2,$ the total jump ratio given by the product over all break points $b$ of the jump ratios $\\sigma_{f_{i}}(b)$ of $f_{i}$.\n  We prove, that for circle homeomorphisms $f_{i}, i=1,2$, which ar"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.5732","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"}