2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/79110We study a connection between the isochronicity of a center of a polynomial vector field and the existence of a polynomial commuting system. We demonstrate an isochronous system of degree 4 which does not commute with any polynomial system. We prove that among the Newton polynomial systems only the Lienard and Abel systems may commute with transversal polynomial fields. We give a full and constructive description of centralizers of the Abel polynomial systems. We give new examples of isochronous systems.21 pages, LaTeX, 5 PostScript FiguresDynamical Systems34C05text