On the rates of convergence of orbits in semigroups of holomorphic functions

2025/03/26 by Betsakos, Dimitrios, Cruz-Zamorano, Francisco J., Zarvalis, Konstantinos · 3 citations
#31A15 #37F44 #Complex Variables (math.CV) #FOS: Mathematics #Primary: 30D05 #Secondary: 30C85

paper · doi:10.48550/arxiv.2503.20388

Abstract

Let (ϕ_t) be a continuous semigroup of holomorphic self-maps of the unit disk \mathbbD with Denjoy-Wolff point τ∈\mathbbD. We study the rate of convergence of the forward orbits of (ϕ_t) to the Denjoy-Wolff point by finding explicit bounds for the quantity |ϕ_t(z)-τ|, z∈\mathbbD, t > 0. We further discuss the corresponding rate of convergence for the backward orbits of (ϕ_t).

Cited by

• From discrete iteration in the unit disc to continuous semigroups of holomorphic functions
• Extremal rate of convergence in discrete hyperbolic and parabolic dynamics
• On frequencies of parabolic Koenigs domains

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