Universal centers in the cubic trigonometric Abel equation
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Date
2014
Authors
Giné, Jaume
Grau Montaña, Maite
Santallusia Esvert, Xavier
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Abstract
We study the center problem for the trigonometric Abel equation dρ/dθ=a1(θ)ρ2+a2(θ)ρ3,dρ/dθ=a1(θ)ρ2+a2(θ)ρ3, where a1(θ)a1(θ) and a2(θ)a2(θ) are cubic trigonometric polynomials in θθ. This problem is closely connected with the classical Poincaré center problem for planar polynomial vector fields. A particular class of centers, the so-called universal centers or composition centers, is taken into account. An example of non-universal center and a characterization of all the universal centers for such equation are provided.
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Electronic Journal of Qualitative Theory of Differential Equations, 2014, núm. 1, p. 1-7