Topological pressure and the variational principle for amenable group action from dimensional point of view

The notion of topological pressure was introduced by Ruell and also he formulated a variational principle for the topological pressure. Pesin introduced a de?nition of topological on subsets inspired by Hausdor? dimension in[6]. In this paper, we considered the topological pressure from dimensional point of view for amenable group action and show that under the tempered condition, we get the variational principle for topological pressure.