We 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.
Global bifurcations of limit cycles in a Holling-type dynamical system
Transversal conics and the existence of limit cycles
Numerical periodic normalization for codim 2 bifurcations of limit cycles with center manifold of dimension higher than 3
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