Cyclicity of elementary polycycles with fixed number of singular points in generic 𝑘-parameter families

Kaleda, P.; Shchurov, I.

doi:10.1090/S1061-0022-2011-01158-6

Cyclicity of elementary polycycles with fixed number of singular points in generic $k$-parameter families
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by P. I. Kaleda and I. V. Shchurov
Translated by: N. Yu. Netsvetaev

St. Petersburg Math. J. 22 (2011), 557-571

DOI: https://doi.org/10.1090/S1061-0022-2011-01158-6

Published electronically: May 2, 2011

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Abstract:

An estimate is found for the number of limit cycles arising from polycycles in generic finite-parameter families of differential equations on the two-sphere. It is proved that if the polycycles have a fixed number of singular points and all the singular points are elementary, then an estimate of cyclicity holds true, which is polynomial in the number of parameters of the family.

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