{"paper":{"title":"Rational functions with identical measure of maximal entropy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Hexi Ye","submitted_at":"2012-11-19T05:07:26Z","abstract_excerpt":"We discuss when two rational functions $f$ and $g$ can have the same measure of maximal entropy. The polynomial case was completed by (Beardon, Levin, Baker-Eremenko,Schmidt-Steinmetz, etc., 1980s-90s), and we address the rational case following Levin-Przytycki (1997). We show: $\\mu_f = \\mu_g$ implies that $f$ and $g$ share an iterate ($f^n = g^m$ for some $n$ and $m$) for general $f$ with degree $d \\geq 3$. And for generic $f\\in \\Rat_{d\\geq 3}$, $\\mu_f = \\mu_g$ implies $g=f^n$ for some $n \\geq 1$. For generic $f\\in \\Rat_2$, $\\mu_f = \\mu_g$ implies that $g= f^n$ or $\\sigma_f\\circ f^n$ for some"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.4303","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"}