Published articles

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37 p, 871.8 KB An inverse approach to the center-focus problem for polynomial differential system with homogenous nonlinearities / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Ramírez, Rafael Orlando (Universitat Rovira i Virgili. Departament d'Enginyeria Informàtica i Matemàtiques) ; Ramírez, Valentín (Universitat de Barcelona)
We consider polynomial vector fields of the form \[ \X=(-y X_m) x (x Y_m) y, \] where X_m=X_m(x,y) and Y_m=Y_m(x,y) are homogenous polynomials of degree m. It is well--known that \X has a center at the origin if and only if \X has an analytic first integral of the form \[ H=12(x^2 y^2) _j=3^ H_j, \] where H_j=H_j(x,y) is a homogenous polynomial of degree j. [...]
2017 - 10.1016/j.jde.2017.04.030
Journal of differential equations, Vol. 263 (2017) , p. 3327-3369  

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