Limit cycle bifurcations of a general Liénard system with polynomial restoring and damping functions (Q1930635)

Consider the system \[ \dot{x}=y, \dot{y}=-x(1+\beta_{1}x+\dotsb+\beta_{2l}x^{2l})+y(\alpha_{0}+\alpha_{1}x+\dotsb+\alpha_{2k}x^{2k}). \] By using a canonical system and applying field rotation parameters, the author proves that the system has at most \(k+l\) limit cycles; \(k\) of them are surrounding the origin and the other \(l\) limit cycles surround one by one the other singularities.