Algaba Durán, AntonioReyes Columé, ManuelGiné, Jaume2025-10-282025-10-282025Algaba, Antonio, Reyes, Manuel and Giné, Jaume. "Local analytic integrability for a class of degenerate planar vector fields" Advanced Nonlinear Studies, vol. 25, no. 3, 2025, pp. 921-934. https://doi.org/10.1515/ans-2023-01842169-0375https://hdl.handle.net/10272/27264Using the normal form theory and the existence of an algebraic inverse integrating factor we characterize the local analytic integrability of the systems whose quasi-homogeneous leading term is (a1 y3 + a2x3 y, b1x5 + b2x2 y2). More specifically we prove that the analytic integrable vector fields inside such family are orbitally equivalent to a semi-quasi-homogeneus system, that is, are not orbitally equivalent to its lowest-degree quasi-homogeneous term.engLocal analytic integrabilityNormal formAlgebraic inverse integratingAnalytic vector fieldsjournal article10.1515/ans-2023-0184open access12 Matemáticas