## 邱家豪: Polynomial orbits in totally minimal systems

：邱家豪 博士

In this talk,we will discuss the saturated theorem along polynomials in minimal systems. As an application, the following result is obtained: for a totally minimal system (X, T) and integer polynomials p_1, . . . , p_d, if every non-trivial integer combination of p_1, . . . , p_d is not constant, then there is some point x such that the set {(T^ p_1(n)x, . . . , T^ p_d(n)x) : n \in Z} is dense in X^d.