Algaba Durán, AntonioGarcía García, Cristóbal, MatemáticoReyes Columé, Manuel2025-04-242025-04-242018-08-01Algaba, A., García, C., & Reyes, M. (2018). Analytical integrability problem for perturbations of cubic Kolmogorov systems. In Chaos, Solitons & Fractals (Vol. 113, pp. 1–10). Elsevier BV. https://doi.org/10.1016/j.chaos.2018.05.0110960-07791873-2887 (electrónico)https://hdl.handle.net/10272/25428We solve, by using normal forms, the analytic integrability problem for differential systems in the plane whose first homogeneous component is a cubic Kolmogorov system being the origin an isolated singularity. As an application, we give the analytically integrable systems of a class of systems x' = x(P2 + P3); y' = y(Q2 +Q3); being Pi;Qi homogeneous polynomials of degree i. We also prove that for any n>=3, there are analytically integrable perturbations of x' = xPn; y' = yQn which are not orbital equivalent to its first homogeneous component.engAtribución-SinDerivadas 3.0 Españahttp://creativecommons.org/licenses/by-nd/3.0/es/Quadratic and cubic systemsKolmogorov systemsIntegrabilityLinearizationInverse Integrating Factorsjournal article10.1016/j.chaos.2018.05.011open access1206.02 Ecuaciones Diferenciales