Limit Cycles and the Distribution of Zeros of Families of Analytic Functions

Details Limit Cycles and the Distribution of Zeros of Families of Analytic Functions Limit Cycles and the Distribution of Zeros of Families of Analytic Functions

1999-08-23

arxiv.org/abs/math/9908122v1

Mathematics

Dynamical Systems

Scientific paper

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.

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