{"paper":{"title":"Singular SRB measures for a non 1--1 map of the unit square","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Abraham Boyarsky, Pawel G\\'ora, Zhenyang Li","submitted_at":"2016-07-06T15:08:09Z","abstract_excerpt":"We consider a map of the unit square which is not 1--1, such as the memory map studied in \\cite{MwM1}. Memory maps are defined as follows: $x_{n+1}=M_{\\alpha}(x_{n-1},x_{n})=\\tau (\\alpha \\cdot x_{n}+(1-\\alpha )\\cdot x_{n-1}),$ where $\\tau$ is a one-dimensional map on $I=[0,1]$ and $0<\\alpha <1$ determines how much memory is being used. In this paper we let $\\tau $ to be the symmetric tent map. To study the dynamics of $M_\\alpha$, we consider the two-dimensional map $$ G_{\\alpha }:[x_{n-1},x_{n}]\\mapsto [x_{n},\\tau (\\alpha \\cdot x_{n}+(1-\\alpha )\\cdot x_{n-1})]\\, .$$ The map $G_\\alpha$ for $\\al"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.01658","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"}