The first return map for planar vector fields with nilpotent linear part with a center or a focus

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/230918The return map for planar vector fields with nilpotent linear part (having a center or a focus and under an assumption generically satisfied) is found as a convergent power series whose terms can be calculated iteratively. The first nontrivial coefficient is the value of an Abelian integral, and the following ones are explicitly given as iterated integrals built with algebraic functions.15 pagesClassical Analysis and ODEs34C05; 34C07The first return map for planar vector fields with nilpotent linear part with a center or a focustext