{"paper":{"title":"Renormalization of circle diffeomorphisms with a break-type singularity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Habibulla Akhadkulov, Mohd Salmi Md Noorani, Sokhobiddin Akhatkulov","submitted_at":"2015-10-12T09:48:31Z","abstract_excerpt":"Let $f$ be an orientation-preserving circle diffeomorphism with irrational rotation number and with a break point $\\xi_{0},$ that is, its derivative $f'$ has a jump discontinuity at this point. Suppose that $f'$ satisfies a certain Zygmund condition dependent on a parameter $\\gamma>0.$ We prove that the renormalizations of $f$ are approximated by M\\\"{o}bius transformations in $C^{1}$-norm if $\\gamma\\in (0,1]$ and they are approximated in $C^{2}$-norm if $\\gamma\\in (1,+\\infty).$ It is also shown, that the coefficients of M\\\"{o}bius transformations get asymptotically linearly dependent."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.03202","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"}