{"paper":{"title":"Tips of Tongues in the Double Standard Family","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Adam Epstein, Jordi Canela, Kuntal Banerjee, Xavier Buff","submitted_at":"2019-03-05T12:51:27Z","abstract_excerpt":"We answer a question raised by Misiurewicz and Rodrigues concerning the family of degree 2 circle maps $F_\\lambda:\\mathbb{R}/\\mathbb{Z}\\to \\mathbb{R}/\\mathbb{Z}$ defined by \\[F_\\lambda(x) := 2x + a+ \\frac{b}{\\pi} \\sin(2\\pi x){\\quad\\text{with}\\quad} \\lambda:=(a,b)\\in \\mathbb{R}/\\mathbb{Z}\\times (0,1).\\] We prove that if $F_\\lambda^{\\circ n}-{\\rm id}$ has a zero of multiplicity $3$ in $\\mathbb{R}/\\mathbb{Z}$, then there is a system of local coordinates $(\\alpha,\\beta):W\\to \\mathbb{R}^2$ defined in a neighborhood $W$ of $\\lambda$, such that $\\alpha(\\lambda) =\\beta(\\lambda)=0$ and $F_\\mu^{\\circ n}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.01795","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"}