{"paper":{"title":"Topological invariants for semigroups of holomorphic self-maps of the unit disc","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.CV","authors_text":"Filippo Bracci, Manuel D. Contreras, Santiago Diaz-Madrigal","submitted_at":"2015-06-28T06:43:23Z","abstract_excerpt":"Let $(\\varphi_t)$, $(\\phi_t)$ be two one-parameter semigroups of holomorphic self-maps of the unit disc $\\mathbb D\\subset \\mathbb C$. Let $f:\\mathbb D \\to \\mathbb D$ be a homeomorphism. We prove that, if $f \\circ \\phi_t=\\varphi_t \\circ f$ for all $t\\geq 0$, then $f$ extends to a homeomorphism of $\\bar{\\mathbb D}$ outside exceptional maximal contact arcs (in particular, for elliptic semigroups, $f$ extends to a homeomorphism of $\\bar{\\mathbb D}$). Using this result, we study topological invariants for one-parameter semigroups of holomorphic self-maps of the unit disc."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.08365","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"}