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A convex analysis approach to the metric mean dimension: limits of scaled pressures and variational principles.(English)Zbl 1537.37041

The authors introduce the notion of upper metric mean dimension of a one-parameter family of scaled pressure functions, which extends the corresponding notion for a single potential due toM. Tsukamoto [Adv. Math. 361, Article ID 106935, 53 p. (2020;Zbl 1436.37032)]. Some of its properties are established, particularly a variational principle in terms of Katok entropy. The end of paper deals with some applications and open questions.

MSC:

37D35 Thermodynamic formalism, variational principles, equilibrium states for dynamical systems
28D20 Entropy and other invariants
37B40 Topological entropy
26A51 Convexity of real functions in one variable, generalizations

Citations:

Zbl 1436.37032

Cite

References:

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[2]Biś, A.; Carvalho, M.; Mendes, M.; Varandas, P.; Zhong, X., Correction: a convex analysis approach to entropy functions, variational principles and equilibrium states. Commun. Math. Phys., 3, 3335-3342 (2023) ·Zbl 07719646
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[17]Lindenstrauss, E.; Tsukamoto, M., Double variational principle for mean dimension. Geom. Funct. Anal., 1048-1109 (2019) ·Zbl 1433.37025
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[21]Shi, R., Finite mean dimension and marker property. Trans. Am. Math. Soc. (June 2023), electronically published ·Zbl 1527.37008
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[25]Tsukamoto, M., Double variational principle for mean dimension with potential. Adv. Math. (2020) ·Zbl 1436.37032
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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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