To investigate the complexity of topological dynamical systems, Köhler introduced the notion of tameness. In this talk, we will focus on the structural theorem for minimal multiple-tame systems.

A key breakthrough in the theory of tame systems came from the work of Glasner, who showed that in a minimal tame system with an invariant measure, the factor map to the maximal equicontinuous factor is almost one-to-one. Building on the characterization of tame systems via independence sets-specifically, that a system is tame if and only if it contains no essential 2-IT-tuples, as established by Kerr and Li-Fuhrmann, Glasner, Jäger, and Oertel resolved an open question of Glasner by proving that this factor map is, in fact, regular one-to-one.

We will begin by reviewing these structural results for minimal tame systems. Then we will turn to a question by Huang, Lian, Shao, and Ye: If a minimal system with an invariant measure has no essential k-IT-tuples (for some k≥3), does it admit a similar structural theorem? We will present recent progress on this question, based on joint work with Xiangtong Wang, Leiye Xu, and Shuhao Zhang.
Meeting ID: 852 4277 3200 Passcode: 103121