Quasi-geodesics and backward orbits under semigroups of holomorphic functions

2022/07/20 by Konstantinos Zarvalis, Zarvalis, Konstantinos · 1 citation
Mathematics · #30D05 #37F44 #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2207.10110

openalex publication_date 2022/07/20 · openalex created_date 2022/07/23 · openalex updated_date 2026/07/28

Abstract

We explore two properties of backward orbits under semigroups of holomorphic self-maps in the unit disk. First, we prove that regular backward orbits are quasi-geodesics for the hyperbolic distance of the unit disk. Then, we show that backward orbits satisfy a useful property, this time in Euclidean terms.

Cited by

• From discrete iteration in the unit disc to continuous semigroups of holomorphic functions

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