Planar systems and Abel equations

Abstract

<p style='text-indent:20px;'>The aim of this paper is to determine when polynomial planar systems can be reduced to Abel equations. The study is based on earlier works by Christopher, Devlin, Lloyd, and Pearson. The novelty of the approach is that the properties of the functions involved in the change of variables are determined. In particular, a constructive method of obtaining planar systems that can be reduced to Abel equations is provided. With the results obtained, it is possible to obtain new families of planar systems that can be reduced to Abel equations.</p>