Composition conditions in the trigonometric Abel equation
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In this paper we deal with the center problem for the trigonometricAbel equation dρ/dρ =a1(θ)ρ^2+a2(θ)ρ^3; where a1(θ) and a2(θ)are trigonometric polynomials in θ. This problem is closely connectedwith the classical Poincar´e center problem for planar polynomial vectorfields.
Is part ofJournal Of Applied Analysis And Computation, 2013, vol. 3, núm. 2, p. 133-144
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Giné, Jaume; Grau Montaña, Maite; Santallusia Esvert, Xavier (Elsevier, 2015)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 ...
A counterexample to the composition condition conjecture for polynomial Abel differential equations Giné, Jaume; Grau Montaña, Maite; Santallusia Esvert, Xavier (Cambridge University Press, 2019)Polynomial 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 ...
Giné, Jaume; Valls, Claudia (Elsevier, 2017)In this paper we study the center problem for Abel polynomial differential equations of second kind. Computing the focal values and using modular arithmetics and Gröbner bases we find the center conditions for such systems ...