Topological multiple recurrence of weakly mixing minimal systems for generalized polynomials

Abstract

Let $(X,T)$ be a weakly mixing minimal system, $p_1,\cdots ,p_d$ be integer-valued generalized polynomials and $(p_1,p_2,\cdots ,p_d)$ be non-degenerate. Then there exists a residual subset $X_0$ of $X$ such that for all $x\in X_0$ $$\{(T^{p_1(n)}x,\cdots ,T^{p_d(n)}x):n\in \mathbb{Z}\}$$ is dense in $X^d$.

27 pages