{"paper":{"title":"Generalising the logistic map through the $q$-product","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech"],"primary_cat":"nlin.CD","authors_text":"Ernesto P. Borges, Robson W. S. Pessoa","submitted_at":"2011-02-22T20:50:06Z","abstract_excerpt":"We investigate a generalisation of the logistic map as $ x_{n+1}=1-ax_{n}\\otimes_{q_{map}} x_{n}$ ($-1 \\le x_{n} \\le 1$, $0<a\\le2$) where $\\otimes_q$ stands for a generalisation of the ordinary product, known as $q$-product [Borges, E.P. Physica A {\\bf 340}, 95 (2004)]. The usual product, and consequently the usual logistic map, is recovered in the limit $q\\to 1$, The tent map is also a particular case for $q_{map}\\to\\infty$. The generalisation of this (and others) algebraic operator has been widely used within nonextensive statistical mechanics context (see C. Tsallis, {\\em Introduction to No"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.4609","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"}