Packing dimensions of basins in the space of sequences
https://doi.org/10.29235/1561-8323-2020-64-3-263-267
Abstract
We consider a space of infinite signals composed of finite-alphabet letters. Each signal generates a sequence of empirical measures on the alphabet and a 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 the packing dimension is computed for each narrow basin.
About the Authors
V. I. Bakhtin
Belarusian State University
Belarus
Belarus
Bakhtin Victor I. – D. Sc. (Physics and Mathematics), Professor
4, Nezavisimosti Ave., 220030, Minsk
B. Sadok
The John Paul II Catholic University of Lublin
Poland
Poland
Sadok Bruno – Master
1 H, konstantynov Str., 20-708, Lublin
References
1. Billingsley P. Hausdorff dimension in probability theory. Illinois Journal of Mathematics, 1960, vol. 4, no. 2, pp. 187– 209. https://doi.org/10.1215/ijm/1255455863
2. Billingsley P. Hausdorff dimension in probability theory II. Illinois Journal of Mathematics, 1961, vol. 5, no. 2, pp. 291–298. https://doi.org/10.1215/ijm/1255629826
3. Bakhtin V. I., Sadok B. M. Hausdorff dimensions of narrow basins in the space of sequences. Trudy Instituta matematiki = Proceedings of the Institute of Mathematics, 2019, vol. 27, no. 1–2, pp. 3–12 (in Russian).
4. Falconer k. Techniques in Fractal Geometry. Chichester, New york, Weinheim, Brisbane, Singapore, Toronto, John Wiley & Sons, 1997. 256 p.
5. Bakhtin V. The McMillan theorem for colored branching processes and dimensions of random fractals. Entropy, 2014, vol. 16, no. 12, pp. 6624–6653. https://doi.org/10.3390/e16126624
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