{"paper":{"title":"Nonrigidity for circle homeomorphisms with several break points","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Abdelhamid Adouani, Habib Marzougui","submitted_at":"2015-12-10T17:09:08Z","abstract_excerpt":"Let $f$ and $g$ be two class $P$-homeomorphisms of the circle $S^{1}$ with break points singularities. Assume that the derivatives $\\textrm{Df}$ and $\\textrm{Dg}$ are absolutely continuous on every continuity interval of $\\textrm{Df}$ and $\\textrm{Dg}$ respectively. Denote by $C(f)$ the set of break points of $f$. For $c\\in S^{1}$, denote by $\\pi_{s, O_{f}(c)}(f)$ the product of $f-$ jumps in break points lying to the $f-$ orbit of $c$ and by $\\textrm{SO}(f) = \\{O_{f}(c):~c \\in C(f)~\\textrm{and}~\\pi_{s, O_{f}(c)}(f)\\neq 1\\}$, called the set of singular $f$-orbits. The maps $f$ and $g$ are call"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.03327","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"}