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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1310.5784","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-10-22T02:47:32Z","cross_cats_sorted":[],"title_canon_sha256":"ffbe16bfd392dd22f5e1697c45572f195e6ad159622923bed43032a1391a98f7","abstract_canon_sha256":"24467c0babba707760d3441808b5a3e712c1d08548b2b82d1411234db7f5692d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:46:56.534758Z","signature_b64":"NMy/AjovAry4twe5Px5wZ/5VQUEPf/U9/N1/lKehdQtAwOI4njfN/RfCUIWfRk93NxYHPcZC7PURDVd95ugdDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"adea04650ec8e99e217da179bfc2e329ee1e0fa5d7b3f1e761ebf8729eb3a808","last_reissued_at":"2026-05-18T01:46:56.534130Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:46:56.534130Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $x_n=1$. 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