20.500.12556/DKUM-98091 Integrability of polynomial vector fields and a dual problem We investigate the integrability of polynomial vector fields through the lens of duality in parameter spaces. We examine formal power series solutions annihilated by differential operators and explore the properties of the integrability variety in relation to the invariants of the associated Lie group. Our study extends to differential operators on affine algebraic varieties, highlighting the intrinsic connection between these operators and local analytic first integrals. To illustrate the duality, the case of quadratic vector fields is considered in detail. integrabilnost polinomialni sistem invariantno polynomial system of ODEs integrability first order linear PDE multigraded rings invariants true false true Springer Nature Angleški jezik Angleški jezik https://link.springer.com/journal/12346 © The Author(s) 2026 Članek v reviji 2026-05-15 09:06:59 2026-05-15 09:06:59 2026-08-25 09:10:08 0000-00-00 00:00:00 2026 0 0 36 str. Vol. 25, [article no.] 63 2026 0000-00-00 Zaloznikova Objavljeno NiDoloceno 2026-02-10 2026-03-04 2026-03-23 51 278060035 10.1007/s12346-026-01484-2 1662-3592 s12346-026-01484-2.pdf s12346-026-01484-2.pdf 1 96F7E1D084FDDE0298484532CD2CE922 cebdccf2ed2533d8df9798e79e5fc19129b9ae4cd2ce16f78a154e31c2d510ab fd478100-502c-11f1-9c27-00155d0001a1 https://dk.um.si/Dokument.php?lang=slv&id=206117 https://link.springer.com/article/10.1007/s12346-026-01484-2 0 00fa5b76-a054-11f1-a977-00155d0001be https://dk.um.si/Dokument.php?lang=slv&id=210397 Fakulteta za elektrotehniko, računalništvo in informatiko 0 0 0