Hostname: page-component-586b7cd67f-tf8b9 Total loading time: 0 Render date: 2024-11-23T05:09:40.748Z Has data issue: false hasContentIssue false

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
Affiliation:
Department of Mathematics, and Statistics, University of Calgary, Calgary, Alberta, Canada T2N 1N4 [email protected]
Get access

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.

Type
NOTES AND PAPERS
Copyright
© The London Mathematical Society 2003

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

Research supported in part by NSERC