{"paper":{"title":"Bowen's formula for meromorphic functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Anna Zdunik, Bogus{\\l}awa Karpi\\'nska, Krzysztof Bara\\'nski","submitted_at":"2010-07-22T11:08:28Z","abstract_excerpt":"Let $f$ be an arbitrary transcendental entire or meromorphic function in the class $\\mathcal S$ (i.e. with finitely many singularities). We show that the topological pressure $P(f,t)$ for $t > 0$ can be defined as the common value of the pressures $P(f,t, z)$ for all $z \\in \\mathbb C$ up to a set of Hausdorff dimension zero. Moreover, we prove that $P(f,t)$ equals the supremum of the pressures of $f|_X$ over all invariant hyperbolic subsets $X$ of the Julia set, and we prove Bowen's formula for $f$, i.e. we show that the Hausdorff dimension of the radial Julia set of $f$ is equal to the infimu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.3855","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"}