Algaba Durán, AntonioFuentes Díaz, NataliaGarcía García, CristóbalReyes Columé, Manuel2025-05-072025-05-072018-03Algaba, A., Fuentes, N., García, C., & Reyes, M. (2018). Non-formally integrable centers admitting an algebraic inverse integrating factor. In Discrete & Continuous Dynamical Systems - A (Vol. 38, Issue 3, pp. 967–988). American Institute of Mathematical Sciences (AIMS). https://doi.org/10.3934/dcds.20180411078-09471553-5231 (electrónico)https://hdl.handle.net/10272/25451“This article has been published in a revised form in Discrete & Continuous Dynamical Systems [https://doi.org/10.3934/dcds.2018041]. This version is free to download for private research and study only. Not for redistribution, re-sale or use in derivative works.”We study the existence of a class of inverse integrating factor for a family of non-formally integrable systems whose lowest-degree quasi-homogeneous term is a Hamiltonian vector field. Once the existence of an inverse integrating factor is established, we study the systems having a center. Among others, we characterize the centers of the perturbations of the system $-y^3\partial_x+x^3\partial_y$ having an algebraic inverse integrating factor.engAtribución-SinDerivadas 3.0 Españahttp://creativecommons.org/licenses/by-nd/3.0/es/Factores integrantes inversosPeriodic solutionsjournal articleopen access12 Matemáticas