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

Brudnyi, Alexander

Ann. Math. (2) 154, No. 2, 227-243 (2001).

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.

Reviewer: Maoan Han (Shanghai)

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