Talk, One-Day Workshop on Topological Dynamics, Jena, Germany
Abstract. In this talk, I will discuss recent joint work with Leiye Xu and Shuhao Zhang on local notions of complexity for measure-preserving systems under actions of countably infinite discrete groups. The talk will focus on three related notions: sequence entropy tuples, IT tuples, and mean sensitive tuples.
Abstract. For actions of amenable groups, mean equicontinuity is a natural relaxation of equicontinuity obtained by averaging a metric along orbits. It is well known that every such action admits a maximal mean equicontinuous factor. Motivated by earlier work of Qiu and Zhao, Li and Yu introduced the notion of weak sensitivity in the mean for Z-actions to better understand this factor.
Abstract. For actions of amenable groups, mean equicontinuity is a natural relaxation of equicontinuity obtained by averaging a metric along orbits. It is well known that every such action admits a maximal mean equicontinuous factor. Motivated by earlier work of Qiu and Zhao, Li and Yu introduced the notion of weak sensitivity in the mean for Z-actions to better understand this factor.
Abstract. Ergodic theorems play a central role in ergodic theory. However, in many real-world situations we cannot model uncertainty by a single precise probability measure. Instead, one often works with non-additive probabilities such as upper probabilities. In this talk, we study Birkhoff’s ergodic theorem and a subadditive ergodic theorem on capacity-preserving system, and discuss some of their applications. Furthermore, we introduce and investigate the weak mixing for capacity-preserving systems. This is joint work with Chunrong Feng, Wen Huang and Huaizhong Zhao.
Abstract. 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.
Abstract. 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.