Work

On the boundary of an immediate attracting basin of a hyperbolic entire function

Year: 2025

Type: article

Abstract: Let be a transcendental entire function of finite order which has an attracting periodic point of period at least 2. Suppose that the set of singularities of the inverse of is finite and contained in the component of the Fatou set that contains . Under an additional hypothesis, we show that the intersection of with the escaping set of has Hausdorff dimension 1. The additional hypothesis is satisfied for example if has the form with polynomials and and a constant . This generalizes a result of Barański, Karpińska, and Zdunik dealing with the case .

Source: Journal of the London Mathematical Society

DOI: 10.1112/jlms.70085

Authors: Walter Bergweiler, Jie Ding

Institutions: Christian-Albrechts-Universität zu Kiel, Taiyuan University of Technology

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: China Scholarship Council