{"paper":{"title":"Takens' embedding theorem with a continuous observable","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.DS","authors_text":"Yonatan Gutman","submitted_at":"2015-10-20T11:49:30Z","abstract_excerpt":"Let $(X,T)$ be a dynamical system where $X$ is a compact metric space and $T:X\\rightarrow X$ is continuous and invertible. Assume the Lebesgue covering dimension of $X$ is $d$. We show that for a generic continuous map $h:X\\rightarrow[0,1]$, the $(2d+1)$-delay observation map $x\\mapsto\\big(h(x),h(Tx),\\ldots,h(T^{2d}x)\\big)$ is an embedding of $X$ inside $[0,1]^{2d+1}$. This is a generalization of the discrete version of the celebrated Takens embedding theorem, as proven by Sauer, Yorke and Casdagli to the setting of a continuous observable. In particular there is no assumption on the (lower) b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.05843","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"}