{"paper":{"title":"Overlap functions for measures in conformal iterated function systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG","math.PR"],"primary_cat":"math.DS","authors_text":"Eugen Mihailescu, Mariusz Urbanski","submitted_at":"2015-07-31T13:18:30Z","abstract_excerpt":"We study conformal iterated function systems (IFS) $\\mathcal S = \\{\\phi_i\\}_{i \\in I}$ with arbitrary overlaps, and measures $\\mu$ on limit sets $\\Lambda$, which are projections of equilibrium measures $\\hat \\mu$ with respect to a certain lift map $\\Phi$ on $\\Sigma_I^+ \\times \\Lambda$. No type of Open Set Condition is assumed. We introduce a notion of overlap function and overlap number for such a measure $\\hat \\mu$ with respect to $\\mathcal S$; and, in particular a notion of (topological) overlap number $o(\\mathcal S)$. These notions take in consideration the $n$-chains between points in the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.08871","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"}