A counterexample to the composition condition conjecture for polynomial Abel differential equations

Abstract

Polynomial Abel differential equations are considered a model problem for the classical Poincaré center–focus problem for planar polynomial systems of ordinary differential equations. In the last few decades, several works pointed out that all centers of the polynomial Abel differential equations satisfied the composition conditions (also called universal centers). In this work we provide a simple counterexample to this conjecture.

The authors are partially supported by a MINECO/FEDER grant number MTM2014-53703-P and by an AGAUR (Generalitat de Catalunya) grant number 2014SGR 1204.