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arXiv 2005.056972020-05math.DSmath.MG

Asymptotic expansion in measure and strong ergodicity

Kang Li, Federico Vigolo, Jiawen Zhang

备注：: To appear in Journal of Topology and Analysis

英文摘要：

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.

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