{"paper":{"title":"Value distribution of the sequences of the derivatives of iterated polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.CV","authors_text":"Y\\^usuke Okuyama","submitted_at":"2016-07-27T11:10:14Z","abstract_excerpt":"We establish the equidistribution of the sequence of the averaged pullbacks of a Dirac measure at any value in $\\mathbb{C}\\setminus\\{0\\}$ under the derivatives of the iterations of a polynomials $f\\in\\mathbb{C}[z]$ of degree more than one towards the $f$-equilibrium (or canonical) measure $\\mu_f$ on $\\mathbb{P}^1$. We also show that for every $C^2$ test function on $\\mathbb{P}^1$, the convergence is exponentially fast up to a polar subset of exceptional values in $\\mathbb{C}$. A parameter space analog of the latter quantitative result for the monic and centered unicritical polynomials family i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.08037","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"}