Topological Pressure and the Variational Principle of Noncompact Sets for Amenable Group Actions

Abstract

The notion of topological pressure was introduced by Ruell and also he formulated a variational principle for the topological pressure. Pesin and Pitskel introduced a definition of topological on subsets inspired by Hausdorff dimension. In this paper, we considered the topological pressure of a noncompact subset for amenable group actions and showed that under the tempered condition, we get the variational principle for topological pressure.

arXiv commentThis paper has been withdrawn by the author due to the proof of the upper bound of the theorem