Resolving an error with path-tracing and a 2-to-1 mapping in a work of Jang, So, and Marotta

TL;DR

This paper corrects two significant errors in a previous work on generalized baby Mandelbrot sets with halos, confirming that the main results still hold after the corrections.

Contribution

It identifies and rectifies errors in a prior proof, ensuring the validity of the original main results.

Findings

Errors in the original proof are corrected.

Main results of the original work remain valid.

Clarifies the conditions under which the results hold.

Abstract

We identify two nontrivial errors in the proof of the main results of the work \emph{generalized baby Mandelbrot sets adorned with halos in families of rational maps} by Jang, So, and Marotta. We correct these errors, showing that the main results remain true.