Abstract
The present paper is devoted to the study of scaling sequences that occur in the definition of entropy type invariants. The necessity to distinguish nonstandard sequences with zero entropy leads to a generalization of the entropy of decreasing sequences of measurable partitions. A more refined entropy type invariant, the “scaling” entropy considered by A. M. Vershik is based on the notion of ε-entropy of a metric space with measure. In the present work it is shown that the “scaling” entropy is a generalization of the entropy of decreasing sequences if 2n is taken as the scaling sequence. The scaling entropy of the partition into the pasts of the (T,T -1)-endomorphisms is calculated. Bibliography: 11 titles.
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Gorbulsky, A. Interrelations Between Various Definitions of the Entropy of Decreasing Sequences of Partitions; Scaling. Journal of Mathematical Sciences 121, 2319–2325 (2004). https://doi.org/10.1023/B:JOTH.0000024613.90346.6e
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DOI: https://doi.org/10.1023/B:JOTH.0000024613.90346.6e