{"paper":{"title":"On conjugations of circle homeomorphisms with two break points","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Akhtam Dzhalilov, Dieter Mayer, Habibulla Akhadkulov","submitted_at":"2011-10-27T15:51:37Z","abstract_excerpt":"Let $f_i\\in C^{2+\\alpha}(S^1\\setminus \\{a_i,b_i\\}), \\alpha >0, i=1,2$ be circle homeomorphisms with two break points $a_i,b_i$, i.e. discontinuities in the derivative $f_i$, with identical irrational rotation number $rho$ and $\\mu_1([a_1,b_1])= \\mu_2([a_2,b_2])$, where $\\mu_i$ are invariant measures of $f_i$. Suppose the products of the jump ratios of $Df_1$ and $Df_2$ do not coincide, i.e. $\\frac{Df_1(a_1-0)}{Df_1(a_1+0)}\\times \\frac{Df_1(b_1-0)}{Df_1(b_1+0)}\\neq \\frac{Df_2(a_2-0)}{Df_2(a_2+0)}\\times \\frac{Df_2(b_2-0)}{Df_2(b_2+0)}$. Then the map $\\psi$ conjugating $f_1$ and $f_2$ is a singul"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.6125","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"}