2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/78997We estimate the expected number of limit cycles situated in a neighbourhood of the origin of a planar polynomial vector field. Our main tool is a distributional inequality for the number of zeros of some families of univariate holomorphic functions depending analytically on a parameter. We obtain this inequality by methods of Pluripotential Theory. This inequality also implies versions of a strong law of large numbers and the central limit theorem for a probabilistic scheme associated with the distribution of zeros.Dynamical SystemsComplex VariablesPrimary 34C05. Secondary 31C10, 60F05text