# Continuity of the Green function in meromorphic families of polynomials

## TL;DR

This paper proves that the Green function for a meromorphic family of polynomials exhibits exponential growth near a punctured disk's origin, with a continuous error term, revealing stability properties of the function in complex dynamics.

## Contribution

It establishes the exponential explosion rate and continuity of the Green function in meromorphic polynomial families near marked points.

## Key findings

- Green function explodes exponentially near the origin
- The explosion has a continuous error term
- Results apply to meromorphic families of polynomials

## Abstract

We prove that along any marked point the Green function of a meromorphic family of polynomials parameterized by the punctured unit disk explodes exponentially fast near the origin with a continuous error term.