Compactification and desingularization of spaces of polynomial Liénard equations
This interesting paper presents a good compactification for all spaces of polynomial Liénard systems \[ \dot{x}=y, \qquad \dot{y}=-g(x)-yf(x) \] with \(g(x)\) and \(f(x)\) polynomials of degrees \(m\) and \(n\), respectively. The author shows that it is possible to compactify and desingularize the space of such system for each \((m,n)\) separately by using both Hamiltonian and singular perturbations.
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