A JENSEN INEQUALITY FOR A FAMILY OF ANALYTIC FUNCTIONS AND AN ESTIMATE FOR THE AVERAGE NUMBER OF LIMIT CYCLES
Published online by Cambridge University Press: 20 March 2003
The paper presents an improvement of the author's earlier estimate for the average number of limit cycles of a planar polynomial vector field situated in a neighbourhood of the origin, provided that the field is close enough to a linear centre in a larger neighbourhood. 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.
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