On fractal properties of non-normal numbers with respect to Renyi f-expansions generated by piecewise linear functions

Albeverio S, Kondratiev Y, Nikiforov R, Torbin G (2014)
Bulletin des Sciences Mathématiques 138(3): 440-455.

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Zeitschriftenaufsatz | Veröffentlicht | Englisch
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Abstract / Bemerkung
The paper is devoted to the study of fractal properties of subsets of the set of non-normal numbers with respect to Renyi f -expansions generated by continuous increasing piecewise linear functions defined on [0, +infinity). All such expansions are expansions for real numbers generated by infinite linear IFS f = {f(0),f(1),..fn,...} with the following list of ratios Q infinity = (q(0),q(1)...qn,....). We prove the superfractality of the set of Q infinity-essentially non-normal numbers, i.e. real numbers having no asymptotic frequencies of any digits from the alphabet A = {0, 1,, n,...}, for any infinite stochastic vector Q infinity, independently of the finiteness resp. infiniteness of its entropy and independently of the faithfulness resp. non-faithfulness of the family of cylinders generated by these expansions. (C) 2013 Elsevier Masson SAS. All rights reserved.
Erscheinungsjahr
Zeitschriftentitel
Bulletin des Sciences Mathématiques
Band
138
Ausgabe
3
Seite(n)
440-455
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Albeverio S, Kondratiev Y, Nikiforov R, Torbin G. On fractal properties of non-normal numbers with respect to Renyi f-expansions generated by piecewise linear functions. Bulletin des Sciences Mathématiques. 2014;138(3):440-455.
Albeverio, S., Kondratiev, Y., Nikiforov, R., & Torbin, G. (2014). On fractal properties of non-normal numbers with respect to Renyi f-expansions generated by piecewise linear functions. Bulletin des Sciences Mathématiques, 138(3), 440-455. doi:10.1016/j.bulsci.2013.10.005
Albeverio, S., Kondratiev, Y., Nikiforov, R., and Torbin, G. (2014). On fractal properties of non-normal numbers with respect to Renyi f-expansions generated by piecewise linear functions. Bulletin des Sciences Mathématiques 138, 440-455.
Albeverio, S., et al., 2014. On fractal properties of non-normal numbers with respect to Renyi f-expansions generated by piecewise linear functions. Bulletin des Sciences Mathématiques, 138(3), p 440-455.
S. Albeverio, et al., “On fractal properties of non-normal numbers with respect to Renyi f-expansions generated by piecewise linear functions”, Bulletin des Sciences Mathématiques, vol. 138, 2014, pp. 440-455.
Albeverio, S., Kondratiev, Y., Nikiforov, R., Torbin, G.: On fractal properties of non-normal numbers with respect to Renyi f-expansions generated by piecewise linear functions. Bulletin des Sciences Mathématiques. 138, 440-455 (2014).
Albeverio, Sergio, Kondratiev, Yuri, Nikiforov, Roman, and Torbin, Grygoriy. “On fractal properties of non-normal numbers with respect to Renyi f-expansions generated by piecewise linear functions”. Bulletin des Sciences Mathématiques 138.3 (2014): 440-455.