2013/03/21 by Filippo Bracci, Bracci, Filippo, Manuel D. Contreras +6
Mathematics · #30C35 #30C80 #37C25 #37F99 #Analytic and geometric function theory #Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics #Holomorphic and Operator Theory #Meromorphic and Entire Functions #Primary 37C10 #Secondary 30D05 #math.CV #math.DS #msc:30C35 #msc:30C80 #msc:30D05 #msc:37C10 #msc:37C25 #msc:37F99
paper · pdf · doi:10.48550/arxiv.1303.5216
28 pages
arxiv created 2013/03/21 · openalex publication_date 2013/03/21 · arxiv updated 2013/03/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We characterize regular fixed points of evolution families in terms of analytical properties of the associated Herglotz vector fields and geometrical properties of the associated Loewner chains. We present several examples showing the rôle of the given conditions. Moreover, we study the relations between evolution families and Herglotz vector fields at regular contact points and prove an embedding result for univalent self-maps of the unit disc with a given boundary regular fixed point into an evolution family with prescribed boundary data.