| We prove the L2-convergence of polynomial ergodic averages of multiple commuting transformations for totally ergodic systems. We show that for each set of polynomials, each average is controlled by a particular characteristic factor introduced by Host and Kra, which is an inverse limit of nilsystems. We then investigate for which sets of four polynomials, the Kronecker factor is characteristic for Weyl systems. We provide an approach to generalize a recurrence theorem of Khintchine for such sets of polynomials. |
