{"paper":{"title":"On the K\\\"onigs function of semigroups of holomorphic self-maps of the unit disc","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Filippo Bracci, Manuel D. Contreras, Santiago D\\'iaz-Madrigal","submitted_at":"2018-04-27T12:28:51Z","abstract_excerpt":"Let $(\\phi_t)$ be a semigroup of holomorphic self-maps of~$\\mathbb D$. In this note, we use an abstract approach to define the K\\\"onigs function of $(\\phi_t)$ and \"holomorphic models\" and show how to deduce the existence and properties of the infinitesimal generator of $(\\phi_t)$ from this construction."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.10465","kind":"arxiv","version":1},"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"}