Work

Criteria for extension of commutativity to fractional iterates of holomorphic self‐maps in the unit disc

Year: 2025

Type: article

Abstract: Let be a univalent non‐elliptic self‐map of the unit disc and let be a continuous one‐parameter semigroup of holomorphic functions in such that commutes with . This assumption does not imply that all elements of the semigroup commute with . In this paper, we provide a number of sufficient conditions that guarantee that for all : This holds, for example, if and have a common boundary (regular or irregular) fixed point different from their common Denjoy–Wolff point , or when has a boundary regular fixed point at which is isogonal, or when has an unrestricted limit at . In addition, we analyze how behaves in the petals of the semigroup .

Source: Journal of the London Mathematical Society

DOI: 10.1112/jlms.70077

Authors: Manuel D. Contreras, Santiago Díaz‐Madrigal, Pavel Gumenyuk

Institutions: Universidad de Sevilla, Politecnico di Milano

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,930

Funder: Istituto Nazionale di Alta Matematica "Francesco Severi"