3 problems

Let $P=(p_1,\b7dots,p_r)$ be a system of rationally independent polynomials, and let $Z_k(X)$ denote the factor appearing in the definition of an $\b7IP\b7rat$-characteristic facto…

Let $T_1,\ldots,T_\ell$ be the commuting, invertible measure-preserving transformations and $p_1,\ldots,p_\ell\in\mathbb{Z}[t]$ the polynomial iterates occurring in Theorem. Let…

Let $p_1,\ldots,p_\ell\in\mathbb{Z}[t]$ be the polynomial iterates, and let the conclusion of Theorem denote the asserted characteristic-factor property for the associated multiple…