Weak expansiveness for actions of sofic groups

摘要

In this paper, we shall introduce h-expansiveness and asymptotical h-expansiveness for actions of sofic groups. By definition, each h-expansive action of a sofic group is asymptotically h-expansive. We show that each expansive action of a sofic group is h-expansive, and, for any given asymptotically h-expansive action of a sofic group, the entropy function (with respect to measures) is upper semi-continuous and hence the system admits a measure with maximal entropy.