{"paper":{"title":"Integrability and non-integrability of periodic non-autonomous Lyness recurrences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Anna Cima, Armengol Gasull, V\\'ictor Ma\\~nosa","submitted_at":"2010-12-22T10:18:21Z","abstract_excerpt":"This paper studies non-autonomous Lyness type recurrences of the form $x_{n+2}=(a_n+x_{n+1})/x_{n}$, where $\\{a_n\\}$ is a $k$-periodic sequence of positive numbers with primitive period $k$. We show that for the cases $k\\in\\{1,2,3,6\\}$ the behavior of the sequence $\\{x_n\\}$ is simple (integrable) while for the remaining cases satisfying this behavior can be much more complicated (chaotic). We also show that the cases where $k$ is a multiple of 5 present some different features."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.4925","kind":"arxiv","version":2},"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"}