On the Formal Integrability Problem for Planar Differential Systems

Abstract

We study the analytic integrability problem through the formal integrability problem and we show its connection, in some cases, with the existence of invariant analytic (sometimes algebraic) curves. From the results obtained, we consider some families of analytic differential systems in ${ℂ}^2$, and imposing the formal integrability we find resonant centers obviating the computation of some necessary conditions.