{"paper":{"title":"The space of $2$-generator postcritically bounded polynomial semigroups and random complex dynamics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV","math.GT","math.PR"],"primary_cat":"math.DS","authors_text":"Hiroki Sumi","submitted_at":"2014-08-21T10:56:10Z","abstract_excerpt":"We investigate the dynamics of $2$-generator semigroups of polynomials with bounded planar postcritical set and associated random dynamics on the Riemann sphere. Also, we investigate the space ${\\cal B}$ of such semigroups. We show that for a parameter $h$ in the intersection of ${\\cal B}$, the hyperbolicity locus ${\\cal H}$ and the closure of the disconnectedness locus (the space of parameters for which the Julia set is disconnected), the corresponding semigroup satisfies either the open set condition (and the Bowen's formula) or that the Julia sets of the two generators coincide. Also, we sh"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.4951","kind":"arxiv","version":8},"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"}