{"paper":{"title":"On the entropy of processes generated by quasifactors","license":"http://creativecommons.org/licenses/by/4.0/","headline":"If a dynamical system has positive entropy, then every full-support quasifactor also has positive entropy.","cross_cats":[],"primary_cat":"math.DS","authors_text":"R\\^omulo M. Vermersch","submitted_at":"2025-11-02T11:22:48Z","abstract_excerpt":"Given a measurable dynamical system $(X,\\mathcal{X},\\mu,T)$, where $X$ is a compact metric space, $\\mathcal{X}$ is the Borel $\\sigma$-algebra on $X$, $\\mu$ is a $T$-invariant Borel probability measure and $T$ is a homeomorphism acting on $X$ we show that, if $h_{\\mu}(T)>0$, then $h_{\\widetilde{\\mu}}(\\widetilde{T})>0$ for every quasifactor $\\widetilde{\\mu}$ of $\\mu$ having full-support."},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"if h_μ(T)>0, then h_μ̃(T̃)>0 for every quasifactor μ̃ of μ having full-support.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The quasifactor μ̃ is required to have full support on the underlying space; without this the entropy positivity may fail.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Positive entropy of a homeomorphism on a compact metric space is inherited by all full-support quasifactors.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"If a dynamical system has positive entropy, then every full-support quasifactor also has positive entropy.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"71b446c0b7251a4084524cbf68d3f8b14aece22d441a1c1ec0432b1dc914eeb0"},"source":{"id":"2511.00891","kind":"arxiv","version":3},"verdict":{"id":"30f163bb-c930-409c-b663-04cbf491290a","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-18T01:26:12.026515Z","strongest_claim":"if h_μ(T)>0, then h_μ̃(T̃)>0 for every quasifactor μ̃ of μ having full-support.","one_line_summary":"Positive entropy of a homeomorphism on a compact metric space is inherited by all full-support quasifactors.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The quasifactor μ̃ is required to have full support on the underlying space; without this the entropy positivity may fail.","pith_extraction_headline":"If a dynamical system has positive entropy, then every full-support quasifactor also has positive entropy."},"references":{"count":32,"sample":[{"doi":"","year":2017,"title":"E. Akin, J. Auslander and A. Nagar,Dynamics of induced systems, Ergodic Theory Dynam. Systems 37(2017), no. 7, 2034–2059","work_id":"3a967d54-3568-4329-afee-f96a785faadb","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1967,"title":"D. V. Anosov,Geodesic flows on closed Riemannian manifolds with negative curvature, Proc. Steklov Inst. Mat. 90 (1967), 1–235","work_id":"3626cbb2-33d0-4207-b7fc-5670c2e43d38","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1975,"title":"W. Bauer and K. Sigmund,Topological dynamics of transformations induced on the space of proba- bility measures, Monatsh. Math.79(1975), 81–92","work_id":"626df333-1f83-41a8-bde9-ea07cd52856d","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2022,"title":"N. C. Bernardes Jr., U. B. Darji and R. M. Vermersch,Uniformly positive entropy of induced trans- formations, Ergodic Theory Dynam. Systems42(2022), 9–18","work_id":"357c5445-8049-441c-8fcd-8a34d92a8b69","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2016,"title":"N. C. Bernardes Jr. and R. M. Vermersch,On the dynamics of induced maps on the space of proba- bility measures, Trans. Amer. Math. Soc.368(2016), no. 11, 7703–7725","work_id":"8bd97499-ec07-4f8d-93b0-6b32fe8ca8de","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":32,"snapshot_sha256":"5d40db4b512a822718867c7ffb1d6303d3718886b0f12bfc410cc9418699ed8e","internal_anchors":0},"formal_canon":{"evidence_count":1,"snapshot_sha256":"8efb2ddb11f6e837401fc64964f61dd0860b8d0b8da54d94e8995100c9a7a69f"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}