Polynomial differential systems with even degree have no global centers (Q2038174)

Consider the real polynomial differential system \[ \frac{dx}{dt}= P(x,y), \; \frac{dy}{dt} = Q(x,y) \tag{1} \] with \( d=\max\{\deg P,\deg Q\}\). An equilibrium point \(p\) of (1) is called a global center if the phase plane is filled with closed orbits surrounding \(p\). It is known that in case \(d=2\) system (1) has no global center. The authors prove that (1) has no global center if \(d\) is even.