PUB - Publikationen an der Universität Bielefeld

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.