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An inverse approach to the center problem / 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 analytic or polynomial vector fields of the form X=(-y+X)∂∂x+(x+Y)∂∂y, where X= X(x, y)) and Y= Y(x, y)) start at least with terms of second order. It is well-known that X has a center at the origin if and only if X has a Liapunov-Poincaré local analytic first integral of the form H=12(x2+y2)+∑j=3∞Hj, where H = H (x, y) is a homogenous polynomial of degree j. [...]
2019 - DOI (Digital Object Identifier)

10.1007/s12215-018-0342-1
Rendiconti del Circolo Matematico di Palermo, Vol. 68, Issue 1 (April 2019) , p. 29-64

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