{"paper":{"title":"Asymptotic behavior of orbits of holomorphic semigroups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.CV","authors_text":"Andrew Zimmer, Filippo Bracci, Herv\\'e Gaussier, Manuel D. Contreras, Santiago D\\'iaz-Madrigal","submitted_at":"2018-10-18T08:39:20Z","abstract_excerpt":"Let $(\\phi_t)$ be a holomorphic semigroup of the unit disc (i.e., the flow of a semicomplete holomorphic vector field) without fixed points in the unit disc and let $\\Omega$ be the starlike at infinity domain image of the Koenigs function of $(\\phi_t)$. In this paper we completely characterize the type of convergence of the orbits of $(\\phi_t)$ to the Denjoy-Wolff point in terms of the shape of $\\Omega$. In particular we prove that the convergence is non-tangential if and only if the domain $\\Omega$ is `quasi-symmetric with respect to vertical axes'. We also prove that such conditions are equi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.07947","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"}