From Abel’s differential equations to Hilbert’s 16th problem

Abstract

The study of the limit cycles of planar polynomial differential equations is motivated both by its appearance in many mathematical models of the real-world as for the second part of Hilbert’s 16th problem. In this work we briefly summarize some results on this subject and we will also highlight the important role that the Abel’s differential equations play in its study. In the way, we recall some nice properties of the Riccati’s differential equations.