{"paper":{"title":"Asymptotically periodic piecewise contractions of the interval","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Arnaldo Nogueira, Benito Pires, Rafael A. Rosales","submitted_at":"2013-10-22T02:47:32Z","abstract_excerpt":"We consider the iterates of a generic injective piecewise contraction of the interval defined by a finite family of contractions. Let $\\phi_i:[0,1]\\to (0,1)$, $1\\le i\\le n$, be $C^2$-diffeomorphisms with $\\sup_{x\\in (0,1)} \\vert D\\phi_i(x)\\vert<1$ whose images $\\phi_1([0,1]), \\ldots, \\phi_n([0,1])$ are pairwise disjoint. Let $0<x_1<\\cdots<x_{n-1}<1$ and let $I_1,\\ldots, I_n$ be a partition of the interval $[0,1)$ into subintervals $I_i$ having interior $(x_{i-1},x_i)$, where $x_0=0$ and $x_n=1$. Let $f_{x_1,\\ldots,x_{n-1}}$ be the map given by $x\\mapsto \\phi_i(x)$ if $x\\in I_i$, for $1\\le i\\le"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.5784","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"}