Geodesic
On a Scaling Entropy Sequence of a Dynamical System
Funkcionalʹnyj analiz i ego priloženiâ, Tome 48 (2014) no. 4, pp. 70-74.

Voir la notice de l'article provenant de la source Math-Net.Ru

We present a series of statements about scaling entropy, a metric invariant of dynamical systems proposed by A. M. Vershik in the late 1990s. We show that this is indeed a metric invariant and calculate it in several special cases.
Keywords: metric invariants, entropy, scaling sequence, $\varepsilon$-entropy. 
@article{FAA_2014_48_4_a6,
     author = {P. B. Zatitskii},
     title = {On a {Scaling} {Entropy} {Sequence} of a {Dynamical} {System}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {70--74},
     publisher = {mathdoc},
     volume = {48},
     number = {4},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2014_48_4_a6/}
}
TY  - JOUR
AU  - P. B. Zatitskii
TI  - On a Scaling Entropy Sequence of a Dynamical System
JO  - Funkcionalʹnyj analiz i ego priloženiâ
PY  - 2014
SP  - 70
EP  - 74
VL  - 48
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FAA_2014_48_4_a6/
LA  - ru
ID  - FAA_2014_48_4_a6
ER  - 
%0 Journal Article
%A P. B. Zatitskii
%T On a Scaling Entropy Sequence of a Dynamical System
%J Funkcionalʹnyj analiz i ego priloženiâ
%D 2014
%P 70-74
%V 48
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FAA_2014_48_4_a6/
%G ru
%F FAA_2014_48_4_a6
P. B. Zatitskii. On a Scaling Entropy Sequence of a Dynamical System. Funkcionalʹnyj analiz i ego priloženiâ, Tome 48 (2014) no. 4, pp. 70-74. http://geodesic.mathdoc.fr/item/FAA_2014_48_4_a6/

[1] A. N. Kolmogorov, Dokl. AN SSSR, 119:5 (1958), 861–864 | MR | Zbl

[2] A. N. Kolmogorov, Dokl. AN SSSR, 124 (1959), 754–755 | MR | Zbl

[3] Ya. G. Sinai, Dokl. AN SSSR, 124 (1959), 768–771 | MR | Zbl

[4] A. G. Kushnirenko, UMN, 22:5(137) (1967), 57–65 | MR | Zbl

[5] T. Kamae, J. Math. Soc. Japan, 24 (1972), 285–306 | DOI | MR | Zbl

[6] F. M. Dekking, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 41:3 (1977/78), 221–239 | DOI | MR

[7] A. M. Vershik, A. D. Gorbulskii, TVP, 52:3 (2007), 446–467 | DOI | MR

[8] M. Queffélec, Substitution Dynamical Systems—Spectral Analysis, Lecture Notes in Math., Springer-Verlag, Berlin, 1294 | MR

[9] A. Vershik, Markov Processes and Related Fields, 16:1 (2010), 169–185 | MR

[10] A. M. Vershik, Algebra i analiz, 23:1 (2011), 111–135 | MR

[11] P. B. Zatitskii, F. V. Petrov, Zap. nauchn. sem. POMI, 390 (2011), 201–209 | MR

[12] A. M. Vershik, P. B. Zatitskiy, F. V. Petrov, Cent. Eur. J. Math., 11:3 (2013), 379–400 | DOI | MR | Zbl