The center problem and composition condition for Abel differential equations
Copyright policy )The center problem and composition condition for Abel differential equations
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
- University of Lleida Spain
Topological structure of integral curves, singular points, limit cycles of ordinary differential equations, Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations, Composition conjecture, Moment conditions, Center problem, composition conjecture, Equacions abelianes, center problem, Composition condition, moment conditions, Abel equations, Periodic solutions to ordinary differential equations, composition condition
Topological structure of integral curves, singular points, limit cycles of ordinary differential equations, Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations, Composition conjecture, Moment conditions, Center problem, composition conjecture, Equacions abelianes, center problem, Composition condition, moment conditions, Abel equations, Periodic solutions to ordinary differential equations, composition condition
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