Algaba Durán, AntonioGarcía García, CristóbalReyes Columé, Manuel2025-05-082025-05-082012-06Algaba, A., García, C., & Reyes, M. (2012). Existence of an inverse integrating factor, center problem and integrability of a class of nilpotent systems. Chaos, Solitons & Fractals, 45(6), 869–878. https://doi.org/10.1016/j.chaos.2012.02.0160960-07791873-2887 (electrónico)https://hdl.handle.net/10272/25456We characterize the nilpotent systems whose lowest degree quasi-homogeneous term is (y,σxn)T, σ=±1, having a formal inverse integrating factor. We prove that, for n even, the systems with formal inverse integrating factor are formally orbital equivalent to (x˙,y˙)T=(y,xn)T. In the case n odd, we give a formal normal form that characterizes them. As a consequence, we give the link among the existence of formal inverse integrating factor, center problem and integrability of the considered systems.engAtribución-SinDerivadas 3.0 Españahttp://creativecommons.org/licenses/by-nd/3.0/es/Factores integrantes inversosLimit cyclesPeriodic solutionsjournal article10.1016/j.chaos.2012.02.016open access12 Matemáticas