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Scaling Entropy of Unstable Systems

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In this paper, we study the slow entropy-type invariant of a dynamic system proposed by A. M. Vershik. We provide an explicit construction of a system that has an empty class of scaling entropy sequences. For this unstable case, we introduce an upgraded notion of the invariant, generalize the subadditivity results, and provide an exhaustive series of examples.

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Authors and Affiliations

  1. Leonhard Euler International Mathematical Institute, St.Petersburg, Russia

    G. A. Veprev

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  1. G. A. Veprev
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Correspondence to G. A. Veprev.

Additional information

Published in Zapiski Nauchnykh Seminarov POMI, Vol. 498, 2020, pp. 5–17.

The work is supported by the Ministry of Science and Higher Education of the Russian Federation, agreement No. 075-15-2019-1619. The work is also supported by the V. A. Rokhlin scholarship for young mathematicians.

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Veprev, G.A. Scaling Entropy of Unstable Systems. J Math Sci 255, 109–118 (2021). https://doi.org/10.1007/s10958-021-05353-y

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  • DOI: https://doi.org/10.1007/s10958-021-05353-y

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