Browsing Articles publicats (Matemàtica) by Subject "Abel equations"
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- ItemOpen AccessA counterexample to the composition condition conjecture for polynomial Abel differential equations(Cambridge University Press, 2019) Giné, Jaume; Grau Montaña, Maite; Santallusia Esvert, XavierPolynomial Abel differential equations are considered a model problem for the classical Poincaré center–focus problem for planar polynomial systems of ordinary differential equations. In the last few decades, several works pointed out that all centers of the polynomial Abel differential equations satisfied the composition conditions (also called universal centers). In this work we provide a simple counterexample to this conjecture.
- ItemOpen AccessThe center problem and composition condition for Abel differential equations(Elsevier, 2015) Giné, Jaume; Grau Montaña, Maite; Santallusia Esvert, XavierThe 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.