In this paper, we give an estimate on the growth of the scaling sequence of the Pascal adic transformation with respect to the sup-metric. We construct a special class of α-names of positive cumulative measure. The linear growth of its cardinality implies the logarithmic growth of the scaling sequence. Bibliography: 14 titles.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 378, 2010, pp. 58–72.
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Lodkin, A.A., Manaev, I.E. & Minabutdinov, A.R. Asymptotic behavior of the scaling entropy of the Pascal adic transformation. J Math Sci 174, 28–35 (2011). https://doi.org/10.1007/s10958-011-0278-x
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DOI: https://doi.org/10.1007/s10958-011-0278-x