{"paper":{"title":"Dynamics of postcritically bounded polynomial semigroups III: classification of semi-hyperbolic semigroups and random Julia sets which are Jordan curves but not quasicircles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV","math.PR"],"primary_cat":"math.DS","authors_text":"Hiroki Sumi","submitted_at":"2008-11-28T03:21:31Z","abstract_excerpt":"We investigate the dynamics of polynomial semigroups (semigroups generated by a family of polynomial maps on the Riemann sphere) and the random dynamics of polynomials on the Riemann sphere. Combining the dynamics of semigroups and the fiberwise (random) dynamics, we give a classification of polynomial semigroups $G$ such that $G$ is generated by a compact family $\\Gamma $, the planar postcritical set of $G$ is bounded, and $G$ is (semi-) hyperbolic. In one of the classes, we have that for almost every sequence $\\gamma \\in \\Gamma ^{\\Bbb{N}}$, the Julia set $J_{\\gamma}$ of $\\gamma $ is a Jordan"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0811.4536","kind":"arxiv","version":5},"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"}