20.500.12556/DKUM-93732 The blow-up method applied to monodromic singularities The blow-up method proves its effectiveness to characterize the integrability of the resonant saddles giving the necessary conditions to have formal integrability and the sufficiency doing the resolution of the associated recurrence differential equation using induction. In this work we apply the blow-up method to monodromic singularities in order to solve the center-focus problem. The case of nondegenerate monodromic singularities is straightforward since any real nondegenerate monodromy singularity can be embedded into a complex system with a resonant saddle. Here we apply the method to nilpotent and degenerate monodromic singularities solving the center problem when the center conditions are algebraic. monodromic singularity blow-up center problem formal first integral monodromna singularnost razpihovanje problem središča formalni prvi integral true false true Angleški jezik Slovenski jezik Znanstveno delo 2025-07-17 03:08:47 2025-08-25 14:31:11 2025-08-26 03:35:34 0000-00-00 00:00:00 2024 0 0 18 str. No. 4 2024 0000-00-00 Zaloznikova Objavljeno NiDoloceno 2023-06-12 0000-00-00 2024-01-08 517.5 181232643 10.14232/ejqtde.2024.1.4 1417-3875 RAZ_Fercec_Brigita_2024.pdf RAZ_Fercec_Brigita_2024.pdf 1 3CB3D10DC36FFB0601305C022A0ED272 5a1681b3b5735142df02111f7085e026daa7d9c4363f22df45568719a101a141 9aeb8cdc-81af-11f0-adee-00155d000105 https://dk.um.si/Dokument.php?lang=slv&id=196236 https://doi.org/10.14232/ejqtde.2024.1.4 0 b4b7cec8-81af-11f0-adee-00155d000105 https://dk.um.si/Dokument.php?lang=slv&id=196237 Fakulteta za energetiko Fakulteta za naravoslovje in matematiko 0 0 0