Complete polynomial vector fields on $\C^2$, Part I

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/65429In this work, under a mild assumption, we give the classification of the complete polynomial vector fields in two variables up to algebraic automorphisms of $\C^2$. The general problem is also reduced to the study of the combinatorics of certain resolutions of singularities. Whereas we deal with $\C$-complete vector fields, our results also apply to $\R$-complete ones thanks to a theorem of Forstneric \cite{forst}.33 pagesDynamical Systems34A20, 32M25, 32J15Complete polynomial vector fields on $\C^2$, Part Itext