{"paper":{"title":"Zero-dimensional isomorphic dynamical models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Lei Jin, Tomasz Downarowicz, Wolfgang Lusky, Yixiao Qiao","submitted_at":"2018-11-06T07:43:47Z","abstract_excerpt":"By an \\emph{assignment} we mean a mapping from a Choquet simplex $K$ to probability measure-preserving systems, obeying some natural restrictions. We prove that if $\\Phi$ is an aperiodic assignment on a Choquet simplex $K$ such that the set of extreme points $\\mathsf{ex}K$ is a countable union $\\bigcup_n E_n$, where each set $E_n$ is compact, zero-dimensional, and the restriction of $\\Phi$ to the Bauer simplex $K_n$ spanned by $E_n$ can be `embedded' in some topological dynamical system, then $\\Phi$ can be `realized' in a zero-dimensional system."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.02206","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"}