On the Topological Entropy of Saturated Sets for Amenable Group Actions

Let (X, G) be a G-action topological system, where G is a countable infinite discrete amenable group and X a compact metric space. We prove a variational principle for topological entropy of saturated sets for systems which have the specification property and uniform separation property. We show that certain algebraic actions satisfy these two conditions. We give an application in multifractal analysis.