This article is cited in 4 papers

Research Papers

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

P. I. Kaleda, I. V. Shchurov

M. V. Lomonosov Moscow State University, Moscow, Russia

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.

Keywords: number of limit cycles, polycycle, Hilbert's sixteenth problem, Hilbert–Arnol'd problem.

Received: 05.07.2009

 English version: St. Petersburg Mathematical Journal, 2011, 22:4, 557–571

Bibliographic databases:

• 
• 
• 
•