Geodesic
Hausdorff dimensions of narrow basins in the space of sequences
Trudy Instituta matematiki, Tome 27 (2019) no. 1, pp. 3-12 
V. I. Bakhtin; B. M. Sadok. Hausdorff dimensions of narrow basins in the space of sequences. Trudy Instituta matematiki, Tome 27 (2019) no. 1, pp. 3-12. http://geodesic.mathdoc.fr/item/TIMB_2019_27_1_a0/
@article{TIMB_2019_27_1_a0,
     author = {V. I. Bakhtin and B. M. Sadok},
     title = {Hausdorff dimensions of narrow basins in the space of sequences},
     journal = {Trudy Instituta matematiki},
     pages = {3--12},
     year = {2019},
     volume = {27},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMB_2019_27_1_a0/}
}
TY  - JOUR
AU  - V. I. Bakhtin
AU  - B. M. Sadok
TI  - Hausdorff dimensions of narrow basins in the space of sequences
JO  - Trudy Instituta matematiki
PY  - 2019
SP  - 3
EP  - 12
VL  - 27
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TIMB_2019_27_1_a0/
LA  - ru
ID  - TIMB_2019_27_1_a0
ER  - 
%0 Journal Article
%A V. I. Bakhtin
%A B. M. Sadok
%T Hausdorff dimensions of narrow basins in the space of sequences
%J Trudy Instituta matematiki
%D 2019
%P 3-12
%V 27
%N 1
%U http://geodesic.mathdoc.fr/item/TIMB_2019_27_1_a0/
%G ru
%F TIMB_2019_27_1_a0

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

We consider a space of infinite signals composed of letters from a finite alphabet. Each signal generates a sequence of empirical measures on the alphabet and the limit set corresponding to this sequence. The space of signals is partitioned into narrow basins consisting of signals with identical limit sets for the empirical measures and for each narrow basin the Hausdorff dimension is computed.

[1] Billingsley P., “Hausdorff dimension in probability theory”, Ill. J. Math., 4 (1960), 187–209

[2] Billingsley P., “Hausdorff dimension in probability theory II”, Ill. J. Math., 5 (1961), 291–298

[3] Bakhtin V., “The McMillan theorem for colored branching processes and dimensions of random fractals”, Entropy, 16:12 (2014), 6624–6653

[4] Young L.-S., “Dimension, entropy and Lyapunov exponents”, Ergod. Theor. Dyn. Syst., 2 (1982), 109–124

[5] Pesin Y. B., Dimension Theory in Dynamical Systems: Contemporary Views and Applications, Chicago University Press, Chicago, 1998