Algaba Durán, AntonioReyes Columé, Manuel2025-04-252025-04-252003-02Algaba, A., & Reyes, M. (2003). Centers with degenerate infinity and their commutators. In Journal of Mathematical Analysis and Applications (Vol. 278, Issue 1, pp. 109–124). Elsevier BV. https://doi.org/10.1016/s0022-247x(02)00625-x1096-0813 (electrónico)0022-247Xhttps://hdl.handle.net/10272/25435We study polynomial systems with degeneracy at infinity and a center-focus equilibrium at the origin. We give some general properties related to the existence of polynomial commutators and use these properties in order to characterize uniformly isochronous polynomial centers with polynomial commutator and, also, we show that the commutator of the centers of the analytic systems whose angular speed is constant can be chosen of radial form. Finally, we characterize the systems (-y + Ps + ∑j=kn-1, xHj, x + Qs + ∑j=kn-1 yHj)t with polynomial commutator, with Pj, Qj, Hj and Kj homogeneous polynomials.engAtribución-SinDerivadas 3.0 Españahttp://creativecommons.org/licenses/by-nd/3.0/es/CentersIsochronous centersCommutatorsjournal article10.1016/s0022-247x(02)00625-xopen access12 Matemáticas