Resumen de Sufficient Conditions to have Global Centers via Branching Theory

Jaume Giné Mesa , Xiao-Song Yang

• It has always been challenging to identify global centers in a planar differential system, despite the recent proposal of a new algorithm to determine such centers. In this paper, we present a novel method for establishing sufficient conditions to achieve a global center. This method is based on determining all the branches that pass through the point at infinity. We apply the method to a specific example to demonstrate how it circumvents the traditional blow-up procedure.