{"paper":{"title":"Entropy and Its Variational Principle for Locally Compact Metrizable Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Andr\\'e Caldas, Mauro Patr\\~ao","submitted_at":"2015-11-06T12:52:54Z","abstract_excerpt":"For a given topological dynamical system $(X,T)$ over a compact set $X$ with a metric $d$, the \"variational principle\" states that \\begin{equation*} \\sup_{\\mu}h_\\mu(T) = h(T) = h_d(T), \\end{equation*} where $h_\\mu(T)$ is the Kolmogorov-Sinai entropy, with the supremum taken over every $T$-invariant probability measure, $h_d(T)$ is the Bowen entropy, and $h(T)$ is the topological entropy as defined by Adler, Konheim and McAndrew. In [9], the concept of topological entropy was adapted for the case where $T$ is a proper map and $X$ is locally compact separable and metrizable, and the variational "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.02057","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"}