Work

On the Rates of Convergence of Orbits in Semigroups of Holomorphic Functions

Year: 2026

Type: article

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

Source: ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE

DOI: 10.2422/2036-2145.202503_027

Authors: Dimitrios Betsakos, Francisco J. Cruz-Zamorano, Konstantinos Zarvalis

Institution: Aristotle University of Thessaloniki

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: bronze

Funders: Ministerio de Ciencia, Innovación y Universidades, Aristotle University of Thessaloniki, Junta de Andalucía

OpenAlex ID: W4416623272

FWCI: 11.39

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Cited by: 1

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