Resumen de Hilbert Number for a Family of Piecewise Nonautonomous Equations

J.L. Bravo, Manuel Fernández García-Hierro, Ignacio Ojeda Martínez de Castilla

• For family x = (a0 + a1 cost + a2 sin t)|x| + b0 + b1 cost + b2 sin t, we solve three basic problems related with its dynamics. First, we characterize when it has a center (Poincaré center focus problem). Second, we show that each equation has a finite number of limit cycles (finiteness problem), and finally we give a uniform upper bound for the number of limit cycles (Hilbert problem 16).