Bifurcation theory for ordinary differential equations, limit cycles, Pertorbació (Matemàtica), Abel equation, Topological structure of integral curves, singular points, limit cycles of ordinary differential equations, Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations, Perturbations, Limit cycles, center variety, Dinàmica combinatòria, perturbations, Periodic orbits, Periodic orbits of vector fields and flows, Equacions abelianes, Periodic solutions to ordinary differential equations, Center variety, Cicles límits, Analysis