Extrema of the Andronov-Hopf function of a polynomial Lienard system (Q2577292)

Consider polynomial Liénard systems of the form \[ {dx\over dt}= y- \sum^{2\ell+1}_{i=1} a_ ix^i,\qquad{dy\over dt}= -x.\tag{\(*\)} \] The authors present a method to study the limit cycles of \((*)\) in case that one of the parameters \(a_i\) in \((*)\) rotates the corresponding vector field. The approach consists in combining the method of generalized Dulac function, the Poincaré function and the Andronov-Hopf function. It is important to note that the extrema of the Andronov-Hopf function correspond to systems with a multiple limit cycle.