{"paper":{"title":"Analytic structures and harmonic measure at bifurcation locus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Grzegorz \\'Swi\\k{a}tek, Jacek Graczyk","submitted_at":"2019-04-20T11:22:19Z","abstract_excerpt":"We study conformal quantities at generic parameters with respect to the harmonic measure on the boundary of the connectedness loci ${\\cal M}_d$ for unicritical polynomials $f_c(z)=z^d+c$. It is known that these parameters are structurally unstable and have stochastic dynamics. We prove $C^{1+\\frac{\\alpha}{d}-\\epsilon}$-conformality, $\\alpha = 2-\\mbox{HD}\\,({\\cal J}_{c_0})$, of the parameter-phase space similarity maps $\\Upsilon_{c_0}(z):\\mathbb{C}\\mapsto \\mathbb{C}$ at typical $c_0\\in \\partial {\\cal M}_d$ and establish that globally quasiconformal similarity maps $\\Upsilon_{c_0}(z)$, $c_0\\in \\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.09434","kind":"arxiv","version":2},"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"}