The scaling entropy of a generic action
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXXIII, Tome 507 (2021), pp. 5-14 Cet article a éte moissonné depuis la source Math-Net.Ru

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We prove that the scaling entropy of a generic action is asymptotically incomparable with a given increasing sublinear sequence.
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G. A. Veprev. The scaling entropy of a generic action. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXXIII, Tome 507 (2021), pp. 5-14. http://geodesic.mathdoc.fr/item/ZNSL_2021_507_a0/

[1] T. Adams, “Genericity and rigidity for slow entropy transformations”, New York J. Math., 27 (2021), 393–416 | MR | Zbl

[2] A. M. Vershik, “Informatsiya, entropiya, dinamika”, Matematika XX veka: vzglyad iz Peterburga, MTsNMO, 2010, 47–76

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

[4] A. M. Vershik, “Masshtabirovannaya entropiya i avtomorfizmy s chisto tochechnym spektrom”, Algebra i analiz, 23:1 (2011), 111–135

[5] A. M. Vershik, P. B. Zatitskiy, F. V. Petrov, “Geometry and dynamics of admissible metrics in measure spaces”, Cent. Eur. J. Math., 11:3 (2013), 379–400 | MR | Zbl

[6] G. A. Veprev, “Scaling entropy of unstable systems”, Zap. nauchn. semin. POMI, 498, 2020, 5–17 | MR

[7] P. B. Zatitskii, “Masshtabiruyuschaya entropiinaya posledovatelnost: invariantnost i primery”, Zap. nauchn. semin. POMI, 432, 2015, 128–161 | Zbl

[8] P. B. Zatitskii, “O vozmozhnoi skorosti rosta masshtabiruyuschei entropiinoi posledovatelnosti”, Zap. nauchn. semin. POMI, 436, 2015, 136–166

[9] P. B. Zatitskii, F. V. Petrov, “O subadditivnosti masshtabiruyuschei entropiinoi posledovatelnosti”, Zap. nauchn. semin. POMI, 436, 2015, 167–173

[10] A. Katok, J.-P. Thouvenot, “Slow entropy type invariants and smooth realization of commuting measure-preserving transformations”, Ann. Inst. H. Poincaré Probab. Statist., 33 (1997), 323–338 | DOI | Zbl

[11] A. Kanigowski, A. Katok, D. Wei, Survey on entropy-type invariants of sub-exponential growth in dynamical systems, 2004, arXiv: 2004.04655

[12] A. G. Kushnirenko, “O metricheskikh invariantakh tipa entropii”, Uspekhi mat. nauk, 22:5 (1967), 57–65 | MR | Zbl

[13] V. V. Ryzhikov, Compact families and typical entropy invariants of measure-preserving actions, arXiv: 2102.06187

[14] S. Ferenczi, “Measure-theoretic complexity of ergodic systems”, Israel J. Math., 100 (1997), 187–207 | DOI | MR