20.500.12556/DKUM-96049 First integrals and invariants of systems of ordinary differential equations We investigate the interplay between monomial first integrals, polynomial invariants of certain group action, and the Poincaré-Dulac normal forms for autonomous systems of ordinary differential equations with a diagonal matrix of the linear part. Using tools from computational algebra, we develop an algorithmic approach for identifying generators of the algebras of monomial and polynomial first integrals, which works in the general case where the matrix of the linear part includes algebraic complex eigenvalues. Our method also provides a practical tool for exploring the algebraic structure of polynomial invariants and their relation to the Poincaré-Dulac normal forms of the underlying vector fields. first integrals polynomial invariants Poincaré-Dulac normal form systems of ordinary differential equations prvi integrali polinomske invariante Poincaré-Dulacova normalna oblika sistemi navadnih diferencialnih enačb true false true Angleški jezik Slovenski jezik Znanstveno delo 2025-11-27 11:00:14 2025-11-27 11:00:14 2025-11-28 03:08:33 0000-00-00 00:00:00 2025 0 0 17 str. št. 21, št. članka 3485 Letn. 13 2025 0000-00-00 Zaloznikova Objavljeno NiDoloceno 2025-10-08 2025-10-22 2025-11-01 517.913 258934531 10.3390/math13213485 2227-7390 RAZ_Grasic_Mateja_2025.pdf RAZ_Grasic_Mateja_2025.pdf 1 31AEC5FD9BBEEC043B2291336B30890C ae7e19333a6049d33059ea708188ce90ce94393be9ec4bcdb52bfbead9e50a99 9498d88f-cb78-11f0-97c8-00155d000105 https://dk.um.si/Dokument.php?lang=slv&id=200916 https://doi.org/10.3390/math13213485 1 e0016273-cb77-11f0-97c8-00155d000105 https://dk.um.si/Dokument.php?lang=slv&id=200915 Fakulteta za naravoslovje in matematiko Fakulteta za elektrotehniko, računalništvo in informatiko 0 0 0