Fast Escaping Sets of meromorphic functions

TL;DR

This paper introduces a new definition for Eremenko's points in meromorphic functions with infinitely many poles and establishes conditions for their existence within narrow annuli using a covering theorem.

Contribution

It provides a novel definition and a new existence condition for Eremenko's points in meromorphic functions with infinitely many poles.

Findings

Defined Eremenko's points for meromorphic functions with infinitely many poles

Established a covering theorem-based condition for existence in narrow annuli

Enhanced understanding of the escaping set structure in complex dynamics

Abstract

In this paper, we give a definition of Eremenko's point of a meromorphic function with infinitely many poles and a condition for its existence in narrow annuli in terms of a covering theorem of annulus.