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Double variational principle for mean dimension with potential.(English)Zbl 1436.37032

Summary: This paper contributes to the mean dimension theory of dynamical systems. We introduce a new concept called mean dimension with potential and develop a variational principle for it. This is a mean dimension analogue of the theory of topological pressure. We consider a minimax problem for the sum of rate distortion dimension and the integral of a potential function. We prove that the minimax value is equal to the mean dimension with potential for a dynamical system having the marker property. The basic idea of the proof is a dynamicalization of geometric measure theory.

MSC:

37C45 Dimension theory of smooth dynamical systems
37B40 Topological entropy
37D35 Thermodynamic formalism, variational principles, equilibrium states for dynamical systems
37A05 Dynamical aspects of measure-preserving transformations

Cite

References:

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This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
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