{"paper":{"title":"Equilibrium measures on saddle sets of holomorphic maps on P^2","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.DS","authors_text":"Eugen Mihailescu, John Erik Fornaess","submitted_at":"2012-03-14T17:05:53Z","abstract_excerpt":"We consider the case of hyperbolic basic sets $\\Lambda$ of saddle type for holomorphic maps $f: \\mathbb P^2\\mathbb C \\to \\mathbb P^2\\mathbb C$. We study equilibrium measures $\\mu_\\phi$ associated to a class of H\\\"older potentials $\\phi$ on $\\Lambda$, and find the measures $\\mu_\\phi$ of iterates of arbitrary Bowen balls. Estimates for the pointwise dimension $\\delta_{\\mu_\\phi}$ of $\\mu_\\phi$ that involve Lyapunov exponents and a correction term are found, and also a formula for the Hausdorff dimension of $\\mu_\\phi$ in the case when the preimage counting function is constant on $\\Lambda$.\n  For "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.3145","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"}