Packing topological entropy for amenable group actions

Abstract Packing topological entropy is a dynamical analogy of the packing dimension, which can be viewed as counterpart Bowen entropy. In present paper we give systematic study for continuous G -action system $(X,G)$ , where X compact metric space and countable infinite discrete amenable group. We first prove variational principle entropy: any Borel subset Z equals supremum upper local over all probability measures has full measure. Then obtain an inequality concerning Finally, show that set generic points invariant measure $\mu $ coincides with if either ergodic or satisfies kind specification property.