METRIC ENTROPY FOR SET-VALUED MAPS

In this article we define a notion of metric entropy for an invariant measure associated to a set-valued map F on a compact metric space X. Besides, we describe its main properties and prove the Half Variational Principle, which relates the metric entropy with the notion of topological entropy given in [13] for this class of maps.

Automated summary

In this article, we introduce a notion of metric entropy for an invariant measure associated with a set-valued map on a compact metric space. We describe its main properties and prove the Half Variational Principle, which establishes the relationship between metric entropy and the notion of topological entropy for this class of maps as given in [13].