{"paper":{"title":"Set-theoretical entropies of generalized shifts","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Fatemah Ayatollah Zadeh Shirazi, Zahra Nili Ahmadabadi","submitted_at":"2017-09-05T20:18:12Z","abstract_excerpt":"In the following text for arbitrary $X$ with at least two elements, nonempty set $\\Gamma$ and self-map $\\varphi:\\Gamma\\to\\Gamma$ we prove the set-theoretical entropy of generalized shift $\\sigma_\\varphi:X^\\Gamma\\to X^\\Gamma$ ($\\sigma_\\varphi((x_\\alpha)_{\\alpha\\in\\Gamma})=(x_{\\varphi(\\alpha)})_{\\alpha\\in\\Gamma}$ (for $(x_\\alpha)_{\\alpha\\in\\Gamma}\\in X^\\Gamma$)) is either zero or infinity, moreover it is zero if and only if $\\varphi$ is quasi-periodic. We continue our study on contravariant set-theoretical entropy of generalized shift and motivate the text using counterexamples dealing with alge"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.01579","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"}