A VARIATIONAL PRINCIPLE OF TOPOLOGICAL PRESSURE ON SUBSETS FOR AMENABLE GROUP ACTIONS

In this paper, we establish a variational principle for topological pressure on compact subsets in the context of amenable group actions. To be precise, for a countable amenable group action on a compact metric space, say G curved right arrow X, for any potential f is an element of C(X), we define and study topological pressure on an arbitrary subset and measure theoretic pressure for any Borel probability measure on X (not necessarily invariant); moreover, we prove a variational principle for this topological pressure on a given nonempty compact subset K subset of X.