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Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/5292

Title: Finite cyclicity of elementary graphics surrounding a focus or center in quadratic systems
Authors: DUMORTIER, Freddy
Guzmann, A.
Roussarie, R.
Issue Date: 2002
Publisher: Birkhäuser Basel
Citation: Qualitative theory of dynamical systems, 3. p. 123-154
Abstract: In this paper we prove that several elementary graphics surrounding a focus or center in quadratic systems have finite cyclicity. This paper represents an additional step in the large program to prove the existence of a uniform bound for the number of limit cycles of a quadratic vector field which we can call the finiteness part of Hilbert's 16th problem for quadratic vector fields. It nearly finishes the part of the program concerned with elementary graphics. In \cite{DRR} this problem was reduced to the proof that 121 graphics have finite cyclicity. The graphics considered here are the hemicycles $(H_4^3)$, $(H_5^3)$ and $(H_6^3)$ together with $(I_{14a}^2)$, $(I_{15a}^2)$, $(I_{15b}^2)$ and $(I_{27}^2)$ in the notation of \cite{DRR}
URI: http://hdl.handle.net/1942/5292
ISSN: 1575-5460
Category: A2
Type: Journal Contribution
Appears in Collections: Research publications

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