20.500.12556/DKUM-97577 Convergence of normalizations for partially integrable differential systems This paper provides some criteria to characterize convergence of normalizations which transform partially integrable analytic differential systems to their Poincaré–Dulac normal forms. For a family of four-dimensional partially integrable differential systems near an equilibrium which has one pair of conjugate imaginary eigenvalues and a pair of resonant nonzero real eigenvalues, we prove convergence of their normalizations. For analytic differential systems with dimension larger than 4, we illustrate that partial integrability may not be sufficient to ensure convergence of the normalizations even though Bruno’s condition � holds. This work generalizes in a natural way the classical results by Poincaré and Lyapunov for a monodromic equilibrium, as well as the one by Moser for a hyperbolic saddle of analytic Hamiltonian systems of one degree of freedom. analytic differential systems normal forms convergence of normalization first integrals resonance diferencialni sistemi konvergenca true false true Elsevier Ltd Angleški jezik Slovenski jezik https://www.sciencedirect.com/journal/nonlinear-analysis Članek v reviji 2026-03-20 12:19:03 2026-03-20 12:19:03 2026-03-21 03:11:28 0000-00-00 00:00:00 2026 0 0 11 str. Vol. 262, [article no.] 113702 January 2026 0000-00-00 Zaloznikova Objavljeno NiDoloceno 2025-03-26 2025-07-04 2025-08-06 51 272163075 10.1016/j.na.2025.113902 1873-5215 1-s2.0-S0362546X25001567-main.pdf 1-s2.0-S0362546X25001567-main.pdf 1 04CA35318DD20FF043B93A2FE89D5FDC b903fc9add52941ea9009568686d417685dc46c0a579ce249fcfbb4c539e5d43 5a54d9cb-244f-11f1-8d16-00155d0001a1 https://dk.um.si/Dokument.php?lang=slv&id=204689 Fakulteta za elektrotehniko, računalništvo in informatiko 0 0 0