## Small amplitude limit cycles and the distribution of zeros of families of analytic functions.(English)Zbl 1010.34021

The paper is concerned with the number of limit cycles of a planar polynomial system in a neighborhood of the origin. An estimation is given on their number. The main tool is a distributional inequality for the number of zeros of some families of univariate holomorphic functions depending analytically on a parameter.

### MSC:

 34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations 34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations 60F05 Central limit and other weak theorems

### Keywords:

small amplitude limit cycles; distribution of zeros
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