A Jensen Inequality for a Family of Analytic Functions
Complex Variables
2007-05-23 v1 Dynamical Systems
Abstract
We improve an estimate (obtained in "A.Brudnyi, Small amplitude limit cycles and the distribution of zeros of families of analytic functions, Ann. of Math. 154 (2) (2001), 227-243") for the average number of limit cycles of a planar polynomial vector field situated in a neighbourhood of the origin provided that the field in a larger neighbourhood is close enough to a linear center. The result follows from a new distributional inequality for the number of zeros of a family of univariate holomorphic functions depending holomorphically on a parameter.
Cite
@article{arxiv.math/0112002,
title = {A Jensen Inequality for a Family of Analytic Functions},
author = {Alex Brudnyi},
journal= {arXiv preprint arXiv:math/0112002},
year = {2007}
}