{"paper":{"title":"$\\Delta$-transitivity for several transformations and an application to the coboundary problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Italo Cipriano, Ryo Moore","submitted_at":"2018-07-27T18:47:47Z","abstract_excerpt":"Given a compact and complete metric space $X$ with several continuous transformations $T_1, T_2, \\ldots T_H: X \\to X,$ we find sufficient conditions for the existence of a point $x\\in X$ such that $(x,x,\\ldots,x)\\in X^H$ has dense orbit for the transformation $$\\mathcal T:=T_1\\times T_2\\times\\cdots\\times T_H.$$\n  We use these conditions together with Liv\\v{s}ic theorem, to obtain that for $\\alpha$-H\\\"older maps $f_1,f_2,\\ldots,f_H: X\\to \\mathbb{R},$ the product $\\prod_{i=1}^H f_i(x_i)$ is a smooth coboundary with respect to $\\mathcal T$ is equivalent to the existence of a non-empty open subset"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.10795","kind":"arxiv","version":4},"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"}