{"paper":{"title":"Conformal measures for meromorphic maps","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":"2016-08-31T10:21:29Z","abstract_excerpt":"In this paper we study the relation between the existence of a conformal measure on the Julia set $J(f)$ of a transcendental meromorphic map $f$ and the existence of zero of the topological pressure function $t \\mapsto P(f, t)$ for the map $f$. In particular, we show that if $f$ is hyperbolic and there exists a $t$-conformal measure which is not totally supported on the set of escaping points, then $P(f, t) = 0$. On the other hand, for a wide class of maps $f$, including arbitrary maps with at most finitely many poles and finite set of singular values and hyperbolic maps with at most finitely "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.08797","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"}