Planar nonautonomous polynomial equations V. The Abel equation

Abstract. We give a full description of the dynamics of the Abel equation \(\dot{z}=z^3+f(t)\) for some special complex valued \(f\). We also prove the existence of at least three periodic solutions for equations of the form \(\dot{z}=z^n+f(t)\) for odd \(n \geq 5\).