Algaba Durán, AntonioCheca Camacho, IsabelGarcía García, CristóbalGiné, Jaume2022-05-182022-05-182016Algaba, A., Checa, I., García, C., & Giné, J. (2016). Analytic integrability inside a family of degenerate centers. In Nonlinear Analysis: Real World Applications (Vol. 31, pp. 288–307). Elsevier BV. https://doi.org/10.1016/j.nonrwa.2016.02.0031468-1218http://hdl.handle.net/10272/20905In this paper we study the analytic integrability around the origin inside a family of degenerate centers or perturbations of them. For this family analytic integrability does not imply formal orbital equivalence to a Hamiltonian system. It is shown how difficult is the integrability problem even inside this simple family of degenerate centers or perturbations of them.engAtribución-NoComercial-SinDerivadas 3.0 Españahttp://creativecommons.org/licenses/by-nc-nd/3.0/es/Nonlinear differential systemsIntegrability problemDegenerate center problemjournal article10.1016/j.nonrwa.2016.02.003open access12 Matemáticas