On the 16th Hilbert Problem

N. Sadovskaia^a, R. Ramirez

^a Polytechnic University of Catalonia, Department of Applied Mathematics II

Abstract: For a polynomial planar vector field of degree $n\geq 3$ with $S$ ($S\geq 2$) invariant nonsingular algebraic curves of degree greater than or equal to two, we proved that the maximal number of algebraic limit cycles is $n-1$. We use the Pontryagin method to analyze the problem of the maximal number of limit cycles for Lienard's equation.

UDC: 517.9

Received in December 2000

Language: English

 English version: Proceedings of the Steklov Institute of Mathematics, 2002, 236, 506–514

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