{"paper":{"title":"Statistical and Deterministic Dynamics of Maps with Memory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Abraham Boyarsky, Harald Proppe, Pawe{\\l} G\\'ora, Zhenyang Li","submitted_at":"2016-04-24T06:22:11Z","abstract_excerpt":"We consider a dynamical system to have memory if it remembers the current state as well as the state before that. The dynamics is defined as follows: $x_{n+1}=T_{\\alpha}(x_{n-1},x_{n})=\\tau (\\alpha \\cdot x_{n}+(1-\\alpha)\\cdot x_{n-1}),$ where $\\tau$ is a one-dimensional map on $I=[0,1]$ and $0<\\alpha <1$ determines how much memory is being used. $T_{\\alpha}$ does not define a dynamical system since it maps $U=I\\times I$ into $I$. In this note we let $\\tau $ to be the symmetric tent map. We shall prove that for $0<\\alpha <0.46,$ the orbits of $\\{x_{n}\\}$ are described statistically by an absolu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.06991","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"}