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Title:
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Centers for generalized quintic polynomial differential systems
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Author:
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Giné, Jaume; Llibre, Jaume; Valls, Claudia
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Notes:
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We classify the centers of polynomial differential systems in $R^2$ of odd degree $d \ge 5$, in complex notation, as $\dot{z} = iz + (z \bar z)^(d-5)/2(A z^5 + B z^4 \bar z + C z^3 \bar z^2 + D z^2 \bar z^3 + E z \bar z^4 + F \bar z^5)$, where $A,B,C,D,E, F \in mathbb{C}$ and either $A = Re(D) = 0$, $A = Im(D) = 0$, $Re(A) = D = 0$ or $Im(A) = D = 0$.
We thank to Professor Colin Christopher for his help in the proof of statement (g) of Theorem 3. The first author is partially supported by a MINECO/ FEDER grant number MTM2014-53703-P and an AGAUR (Generalitat de Catalunya) grant number 2014SGR 1204. The second author is partially supported by a MINECO/ FEDER grant number MTM2008-03437, an AGAUR grant number 2009SGR 410, ICREA Academia, two FP7-PEOPLE-2012-IRSES numbers 316338 and 318999, and FEDERUNAB10-4E-378. The third author is partially supported by FCT/Portugal through the project UID/MAT/04459/2013. |
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Subject(s):
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-Nilpotent center
-Degenerate center
-Lyapunov constants
-Bautin method
-Matemàtica
-Mathematics |
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Rights:
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(c) Rocky Mountain Mathematics Consortium, 2017
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Document type:
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Article
Article - Submitted version |
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Published by:
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Rocky Mountain Mathematics Consortium
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