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

Xiaojun Huang; Zhiqiang Li; Yunhua Zhou

doi:10.3934/dcds.2020146

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2020, Volume 40, Issue 5: 2687-2703. Doi: 10.3934/dcds.2020146

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

College of Mathematics and Statistics, Chongqing University, Chongqing, China 401331

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Received: May 2019

Published online: May 2020

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Abstract

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 $.

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Mathematics Subject Classification: 37A35, 37B40.

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