Topological invariants for semigroups of holomorphic self-maps of the unit disk

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• 作者：Filippo Bracci^a ; ¹ ; ^{fbracci@mat.uniroma2.it} ; Manuel D. Contreras^b ; ² ; ^{contreras@us.es} ; Santiago Dí ; az-Madrigal^b ; ² ; ^{madrigal@us.es}
• 关键词：primary ; 37C10 ; 30C35 ; secondary ; 30D05 ; 30C80 ; 37F99
• 刊名：Journal de Mathématiques Pures et Appliquées
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：107
• 期：1
• 页码：78-99
• 全文大小：553 K
• 卷排序：107

文摘

Let (φt)(φt), (ϕt)(ϕt) be two one-parameter semigroups of holomorphic self-maps of the unit disk D⊂CD⊂C. Let f:D→Df:D→D be a homeomorphism. We prove that, if f∘ϕ_{t=φt∘ff∘ϕt=φt∘f for all t≥0t≥0, then f   extends to a homeomorphism of D‾ outside exceptional maximal contact arcs (in particular, for elliptic semigroups, f   extends to a homeomorphism of D‾). Using this result, we study topological invariants for one-parameter semigroups of holomorphic self-maps of the unit disk.}