报告摘要：We provide several characterizations of systems that are disjoint from all minimal systems. For a topological dynamical system $(X,T)$, it is disjoint from all minimal systems if and only if there exist minimal sets $(M_i)_{i\in\mathbb{N}}$ within $X$ whose union is dense in $X$ and each of which is disjoint from $X$. For a semi-simple system $(X,T)$, it is disjoint from all minimal systems if and only if there exists a dense $G_{\delta}$ set $\Omega$ in $X \times X$ such that for every pair $(x_1,x_2) \in \Omega$, the subsystems $\overline{orb(x_1,T)}$ and $\overline{orb(x_2,T)}$ are disjoint. Furthermore, a similar characterization can be applied to a general system. This work is joint with Wen Huang, Song Shao and Xiangdong Ye.
邀请人：杨大伟