Geodesic
Asymptotic behavior of the scaling entropy of the Pascal adic transformation
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XVIII, Tome 378 (2010), pp. 58-72 
A. A. Lodkin; I. E. Manaev; A. R. Minabutdinov. Asymptotic behavior of the scaling entropy of the Pascal adic transformation. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XVIII, Tome 378 (2010), pp. 58-72. http://geodesic.mathdoc.fr/item/ZNSL_2010_378_a5/
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     title = {Asymptotic behavior of the scaling entropy of the {Pascal} adic transformation},
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     volume = {378},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_2010_378_a5/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

In this paper, we give an estimation for the growth of the scaling sequence of the Pascal adic transformation with respect to the $\sup$-metric. We construct a special class of $\alpha$-names of positive cumulative measure. The linear growth of its cardinality implies the logarithmic growth of the scaling sequence. Bibl. 14 titles.

[1] P. Billingslei, Ergodicheskaya teoriya i informatsiya, Mir, M., 1969 | MR

[2] A. M. Vershik, “Ravnomernaya algebraicheskaya approksimatsiya operatorov sdviga i umnozheniya”, DAN SSSR, 259:3 (1981), 526–529 | MR | Zbl

[3] A. M. Vershik, “Teorema o periodicheskoi markovskoi approksimatsii v ergodicheskoi teorii”, Zap. nauchn. semin. LOMI, 115, 1982, 72–82 | MR | Zbl

[4] A. M. Vershik, “Dinamicheskaya teoriya rosta v gruppakh: entropiya, granitsy, primery”, Uspekhi mat. nauk, 55:4(334) (2000), 59–128 | DOI | MR | Zbl

[5] A. M. Vershik, A. D. Gorbulskii, “Masshtabirovannaya entropiya filtratsii $\sigma$-algebr”, Teor. veroyatn. i ee primen., 52:3 (2007), 446–467 | DOI | Zbl

[6] V. Feller, Vvedenie v teoriyu veroyatnostei i ee prilozheniya, v. 1, Mir, M., 1984 | Zbl

[7] O. Bratteli, “Inductive limits of finite dimensional $C^*$-algebras”, Trans. Amer. Math. Soc., 171 (1972), 195–234 | MR | Zbl

[8] S. Ferenczi, “Measure-theoretic complexity of ergodic systems”, Israel Math. J., 100 (1997), 180–207 | DOI | MR

[9] É. Janvresse, T. de la Rue, “The Pascal adic transformation is loosely Bernoulli”, Ann. Inst. H. Poincaré Probab. Statist., 40:3 (2004), 133–139 | DOI | MR | Zbl

[10] A. A. Lodkin, A. M. Vershik, “Approximation for actions of amenable groups and transversal automorphisms”, Lect. Notes Math., 1132, 1985, 331–346 | DOI | MR | Zbl

[11] X. Mela, K. Petersen, “Dynamical properties of the Pascal adic transformation”, Ergodic Theory Dynam. Systems, 25 (2005), 227–256 | DOI | MR | Zbl

[12] K. Petersen, K. Schmidt, “Symmetric Gibbs measures”, Trans. Amer. Math. Soc., 349:7 (1997), 2775–2811 | DOI | MR | Zbl

[13] A. M. Vershik, “Dynamics of metrics in measure spaces and their asymptotic invariants”, Markov Process. Related Fields, 16:1 (2010), 169–185 | MR

[14] A. M. Vershik, Boundedness of the scaling sequences of the automorphisms with discrete spectrum, 2010, arXiv: 1008.4946v1