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A variational principle of topological pressure on subsets for amenable group actions

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  • 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\curvearrowright X $, for any potential $ f\in 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\subseteq X $.

    Mathematics Subject Classification: 37A35, 37B40.

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