Rational Limit Cycles of Abel Differential Equations

José Luis Bravo Trinidad, Luis Ángel Calderón Pérez, Ignacio Ojeda Martínez de Castilla

We study the number of rational limit cycles of the Abel equation $x^{\prime }=A(t)x^3+B(t)x^2$, where $A(t)$ and $B(t)$ are real trigonometric polynomials. We show that this number is at m…