Asymptotic expansion in measure and strong ergodicity

Autor:	Li, Kang, Vigolo, Federico, Zhang, Jiawen
Rok vydání:	2020
Předmět:	Mathematics - Dynamical Systems Mathematics - Metric Geometry (2020): 37A30 37A15. Secondary: 05C48
Druh dokumentu:	Working Paper
Popis:	In this paper, we introduce and study a notion of asymptotic expansion in measure for measurable actions. This generalises expansion in measure and provides a new perspective on the classical notion of strong ergodicity. Moreover, we obtain structure theorems for asymptotically expanding actions, showing that they admit exhaustions by domains of expansion. As an application, we recover a recent result of Marrakchi, characterising strong ergodicity in terms of local spectral gaps. We also show that homogeneous strongly ergodic actions are always expanding in measure and establish a connection between asymptotic expansion in measure and asymptotic expanders by means of approximating spaces. Comment: To appear in Journal of Topology and Analysis
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2005.05697 Zobrazit plný text záznamu View this record from Arxiv