{"paper":{"title":"A variational principle for topological pressure for certain non-compact sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Daniel Thompson","submitted_at":"2008-09-23T15:26:57Z","abstract_excerpt":"Let $(X,d)$ be a compact metric space, $f:X \\mapsto X$ be a continuous map with the specification property, and $\\varphi: X \\mapsto \\IR$ be a continuous function. We prove a variational principle for topological pressure (in the sense of Pesin and Pitskel) for non-compact sets of the form \\[ \\{x \\in X : \\lim_{n \\ra \\infty} \\frac{1}{n} \\sum_{i = 0}^{n-1} \\varphi (f^i (x)) = \\alpha \\}. \\] Analogous results were previously known for topological entropy. As an application, we prove multifractal analysis results for the entropy spectrum of a suspension flow over a continuous map with specification "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0809.3941","kind":"arxiv","version":1},"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"}