Universitat de Lleida
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.
The authors are partially supported by a MINECO/FEDER grant number MTM2011-22877 and by a Generalitat de Catalunya grant number 2009SGR 381
English
Trigonometria; Trigonometry; Center problem; Abel differential equation; Universal center; Composition condition; Polynomial differential equations
Bolyai Institute. University of Szeged
Hungarian Academy of Sciences
info:eu-repo/grantAgreement/MICINN//MTM2011-22877/ES/BIFURCACIONES, INTEGRABILIDAD Y PROPIEDADES CUALITATIVAS DE FAMILIAS DE CAMPOS VECTORIALES/
Reproducció del document publicat a https://doi.org/10.14232/ejqtde.2014.1.1
Electronic Journal of Qualitative Theory of Differential Equations, 2014, núm. 1, p. 1-7
cc-by (c) Giné, Jaume et al., 2014
https://creativecommons.org/licenses/by/4.0/deed.es_ES
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