{"paper":{"title":"On an entropy of $Z_+^k$-actions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Wenda Zhang, Yujun Zhu","submitted_at":"2013-03-10T09:35:32Z","abstract_excerpt":"In this paper, a definition of entropy for $\\mathbb{Z}_+^k(k\\geq2)$-actions due to S. Friedland \\cite{Friedland} is studied. Unlike the traditional definition, it may take a nonzero value for actions whose generators have finite (even zero) entropy as single transformations. Some basic properties are investigated and its value for the $\\mathbb{Z}_+^k$-actions on circles generated by expanding endomorphisms is given. Moreover, an upper bound of this entropy for the $\\mathbb{Z}_+^k$-actions on tori generated by expanding endomorphisms is obtained via the preimage entropies, which are entropy-lik"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.2299","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"}