Large scaled geometry of Julia sets of entire and meromorphic functions

TL;DR

This paper investigates the large-scale geometric structure of Julia sets for entire and meromorphic functions, revealing how transcendental directions influence their asymptotic behavior near essential singularities.

Contribution

It introduces a new perspective on Julia set geometry by linking asymptotic structure to transcendental directions from a function-theoretic viewpoint.

Findings

Part of the large-scale structure is determined by transcendental directions.

Provides asymptotic descriptions of Julia sets near essential singularities.

Connects geometric structure with function-theoretic properties.

Abstract

In this paper, we study the large scaled geometric structure of Julia sets of entire and meromorphic functions. Roughly speaking, the structure gives us some asymptotic information about the Julia set near the essential singularity. We will show that part of this structure are determined by the transcendental directions coming from function theoretic point of view.