Universitat de Lleida
The classical Poincaré center-focus problem for planar polynomial systems of ordinary differential equations can be transformed, in certain particular cases, to the center problem of a trigonometric Abel differential equation. Several research papers focused on the study of the center problem for trigonometric Abel differential equations. Polynomial Abel differential equations are also considered in the literature as a model problem. In this work we make a survey of the most important results in this context and we provide the state of the art of several related conjectures. We give two new results on these conjectures.
The authors are partially supported by a MINECO/FEDER grant number MTM2014-53703-P and by an AGAUR (Generalitat de Catalunya) grant number 2014SGR 1204
English
Abel equations; Center problem; Composition condition; Moment conditions; Composition conjecture; Equacions abelianes
Elsevier
info:eu-repo/grantAgreement/MINECO//MTM2014-53703-P/ES/METODOS CUALITATIVOS EN SISTEMAS DIFERENCIALES CONTINUOS/
Versió postprint del document publicat a https://doi.org/10.1016/j.exmath.2015.12.002
Expositiones Mathematicae, 2016, vol. 34, núm. 2, p. 210-222
cc-by-nc-nd (c) Elsevier, 2015
https://creativecommons.org/licenses/by-nc-nd/4.0/deed.ca
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