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This result gives as a corollary the Sharkovski\\u{\\i} Theorem for quasiperiodically forced skew-products on the cylinder proved in \\cite{FJJK}.\n  Next, the notion of $s$-horseshoe is defined for quasiperiodically forced skew-products on the cylinder and"},"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":"1411.2759","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-11-11T10:40:45Z","cross_cats_sorted":[],"title_canon_sha256":"feac1b2036eb615a5360b9cbff78f015cb785c6e622a7d8e7995d4e40426fb76","abstract_canon_sha256":"da0bfb91be4bcf1bdaa86b9441f6127045eb7a13bed4894618e99e07d0303e2c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:37:53.122487Z","signature_b64":"majZzSW0C2hyN3Tq78EEnN9IElQqU83El1sFfpQ2NyHPlUwmnM8EgDsfSZQkkE/fQHfn/CximRy4dE4kUpdDDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"27ea70f2b7365e525c7447959873a1224ae3fa0138241db9caea2ab59f36a33f","last_reissued_at":"2026-05-18T02:37:53.121908Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:37:53.121908Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Forcing and entropy of strip patterns of quasiperiodic skew products in the cylinder","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Francesc Ma\\~nosas, Leopoldo Morales, Llu\\'is Alsed\\`a","submitted_at":"2014-11-11T10:40:45Z","abstract_excerpt":"We extend the results and techniques from \\cite{FJJK} to study the combinatorial dynamics (\\emph{forcing}) and entropy of quasiperiodically forced skew-products on the cylinder. 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