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34c07 (primary)

Bulletin of the London Mathematical Society (1)

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A JENSEN INEQUALITY FOR A FAMILY OF ANALYTIC FUNCTIONS AND AN ESTIMATE FOR THE AVERAGE NUMBER OF LIMIT CYCLES
ALEXANDER BRUDNYI
Journal:

Bulletin of the London Mathematical Society / Volume 35 / Issue 2 / March 2003

Published online by Cambridge University Press:

20 March 2003, pp. 229-235

Print publication:

March 2003
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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.