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Ergodicity and Mixing of Invariant Capacities and Applications (University of Science and Technology of China)

Published:

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.

Regional mean sensitivity and the maximal mean equicontinuous factor (IM PAN, Warszawa, Poland)

Published:

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.

Regional mean sensitivity and the maximal mean equicontinuous factor (Jagiellonian University, Kraków, Poland)

Published:

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.