Two limit cycles for quintic Liénard systems

Every classical Liénard system $\dot{x}=y-F(x)$, $\dot{y}=-x$, with F an arbitrary real polynomial of degree at most five, has at most two geometrically distinct isolated periodic orbits, and the bound is attained. This proves the degree-five case of the Lins Neto–de Melo–Pugh conjecture.