Rocky Mountain Journal of Mathematics

Centers for generalized quintic polynomial differential systems

Jaume Giné, Jaume Llibre, and Claudia Valls

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Abstract

We classify the centers of polynomial differential systems in $\mathbb {R}^2$ of odd degree $d \ge 5$, in complex notation, as $ \cdot z = i z + (z \overline z)^{({d-5})/{2}} (A z^5 + B z^4 \overline z + C z^3 \overline z^2+ D z^2 \overline z^3+ E z \overline z^4 + F \overline 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 $\Im (A)=D=0$.

Article information

Source
Rocky Mountain J. Math., Volume 47, Number 4 (2017), 1097-1120.

Dates
First available in Project Euclid: 6 August 2017

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1501984942

Digital Object Identifier
doi:10.1216/RMJ-2017-47-4-1097

Mathematical Reviews number (MathSciNet)
MR3689947

Zentralblatt MATH identifier
1384.34038

Subjects
Primary: 34C05: Location of integral curves, singular points, limit cycles
Secondary: 37C10: Vector fields, flows, ordinary differential equations

Keywords
Nilpotent center degenerate center Lyapunov constants Bautin method

Citation

Giné, Jaume; Llibre, Jaume; Valls, Claudia. Centers for generalized quintic polynomial differential systems. Rocky Mountain J. Math. 47 (2017), no. 4, 1097--1120. doi:10.1216/RMJ-2017-47-4-1097. https://projecteuclid.org/euclid.rmjm/1501984942


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