Hausdorff measure of escaping sets on certain meromorphic functions

2017/05/10 by Wenli Li, Li, Wenli
Mathematics · #Analytic and geometric function theory #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Meromorphic and Entire Functions #math.DS

paper · pdf · doi:10.48550/arxiv.1705.03745

openalex publication_date 2017/05/10 · arxiv created 2017/11/10 · arxiv updated 2017/11/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04

Abstract

We consider transcendental meromorphic function for which the set of finite singularities of its inverse is bounded. Bergweiler and Kotus gave bounds for the Hausdorff dimension of escaping sets if the function has no logarithmic singularities over infinity, the multiplicities of poles are bounded and the order is finite. We study the case of infinite order and find gauge functions for which the Hausdorff measure of escaping sets is zero or infinity.

Citations

• Fractal Geometry: Mathematical Foundations and Applications.

Related

• Hausdorff measure of escaping and Julia sets for bounded type functions of finite order
• The exact value of Hausdorff dimension of escaping sets of class B meromorphic functions
• Hausdorff dimension of elliptic functions with critical values approaching infinity
• Fast Escaping Sets of meromorphic functions
• Dimensions of non-autonomous meromorphic functions of finite order