Polynomial dynamical systems associated with the KdV hierarchy

In 1974, S.P. Novikov introduced the stationary $n$-equations of the Korteweg–de Vries hierarchy, namely the $n$-Novikov equations. These are associated with integrable polynomial dynamical systems, with polynomial $2n$ integrals, in ${ℂ}^{3n}$. In this paper, we construct an infinite-dimensional polynomial dynamical system that is universal for all dynamical systems corresponding to the $n$-Novikov equations. Thus, we solve the well-known problem of the relationship between the $n$-Novikov equations for different $n$.