2008/07/10 by Filippo Bracci, Manuel D. Contreras, Bracci, Filippo +4 · 1 citation
Mathematics · #30C80 #30D05 #34M15 #Advanced Differential Equations and Dynamical Systems #Classical Analysis and ODEs (math.CA) #Complex Variables (math.CV) #FOS: Mathematics #Mathematical Dynamics and Fractals #Meromorphic and Entire Functions #math.CA #math.CV #msc:30C80 #msc:30D05 #msc:34M15
paper · pdf · doi:10.48550/arxiv.0807.1594
41 pages
arxiv created 2008/07/10 · openalex publication_date 2008/07/10 · arxiv updated 2009/12/01 · openalex created_date 2019/07/30 · openalex updated_date 2026/07/28
In this paper we introduce a general version of the Loewner differential equation which allows us to present a new and unified treatment of both the radial equation introduced in 1923 by K. Loewner and the chordal equation introduced in 2000 by O. Schramm. In particular, we prove that evolution families in the unit disc are in one to one correspondence with solutions to this new type of Loewner equations. Also, we give a Berkson-Porta type formula for non-autonomous weak holomorphic vector fields which generate such Loewner differential equations and study in detail geometric and dynamical properties of evolution families.