{"paper":{"title":"Topological Pressure for Locally Compact Metrizable Systems","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Andr\\'e Caldas","submitted_at":"2016-05-05T19:22:21Z","abstract_excerpt":"It is widely known that when $X$ is compact Hausdorff, and when $T: X \\to X$ and $f: X \\to \\mathbb{R}$ are continuous, \\begin{equation*} P(T,f) = \\sup_{\\text{$\\mu$: Radon probability}} \\left( h_\\mu(T) + \\int f\\, \\mathrm{d}\\mu \\right), \\end{equation*} where $P(T,f)$ is the \"topological pressure\" and $h_\\mu(T)$ is the measure theoretic entropy of $T$ with respect to $\\mu$. This result is known as \"variational principle\". We generalize the concept of \"topological pressure\" for the case where $X$ is a separable locally compact metric space. Our definitions are quite similar to those used in the co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.01698","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"}