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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

ALEXANDER BRUDNYI
ALEXANDER BRUDNYI
Affiliation:
Department of Mathematics, and Statistics, University of Calgary, Calgary, Alberta, Canada T2N 1N4 albru@math.ucalgary.ca
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Abstract

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.

Keywords

34C07 (primary)46E15 (secondary)
Type
NOTES AND PAPERS
Information
Bulletin of the London Mathematical Society , Volume 35 , Issue 2 , March 2003 , pp. 229 - 235
Copyright
© The London Mathematical Society 2003

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Footnotes

Research supported in part by NSERC