| Popis: |
For perturbations of integrable non-Hamiltonian quasi-homogeneous planar vector field whose origin is a non-degenerate singular point, orbital linearization and analytic integrability are equivalent. We show a class of analytically integrable vector fields whose origin is a degenerate singular point which is orbitally equivalent to a semi-quasi-homogeneous system, that is, it is not orbital equivalent to its lowest-degree quasi-homogeneous term. The first three authors are partially supported by Ministerio de Economia y Competitividad, Plan Nacional I +D +I co-financed with FEDER funds, in the frame of the project PGC2018-096265-B-I00, and by Consejería de Educación y Ciencia de la Junta de Andalucía (FQM-276, P12-FQM-1658, UHU126150 and P20 00764). The last author is partially supported by the Agencia Estatal de Investigación, Spain grant PID2020-113758GB-I00 and an AGAUR (Generalitat de Catalunya) grant number 2021SGR 01618. |
