{"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. For these maps we prove that a cyclic permutation $\\tau$ forces a cyclic permutation $\\nu$ as interval patterns if and only if $\\tau$ forces $\\nu$ as cylinder patterns. 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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.2759","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"}