{"paper":{"title":"Bifurcation measures and quadratic rational maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Hexi Ye, Laura DeMarco, Xiaoguang Wang","submitted_at":"2014-04-29T16:13:54Z","abstract_excerpt":"We study critical orbits and bifurcations within the moduli space of quadratic rational maps on $\\mathbb{P}^1$. We focus on the family of curves, $Per_1(\\lambda)$ for $\\lambda$ in $\\mathbb{C}$, defined by the condition that each $f\\in Per_1(\\lambda)$ has a fixed point of multiplier $\\lambda$. We prove that the curve $Per_1(\\lambda)$ contains infinitely many postcritically-finite maps if and only if $\\lambda = 0$; addressing a special case of [BD2, Conjecture 1.4]. We also show that the two critical points of a map $f$ define distinct bifurcation measures along $Per_1(\\lambda)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.7417","kind":"arxiv","version":3},"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"}