Universal centers and composition conditions
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In this paper, we characterize the universal centres of the ordinary differential equations , where ai(θ) are trigonometric polynomials, in terms of the composition conditions. These centres are closely related with the classical Poincaré centre problem for planar analytic differential systems. Additionally, we show that the notion of universal centre is not invariant under changes of variables, and we also provide different families of universal centres. Finally, we characterize all the universal centres for the quadratic polynomial differential systems. Universal centres and composition conditions.
Is part ofProceedings of the London Mathematical Society, 2013, vol. 106, núm. 3, p. 481-507
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Giné, Jaume; Grau Montaña, Maite; Santallusia Esvert, Xavier (Shanghai Normal University & Wilmington Scientific Publisher, 2013)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 ...
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 ...