caa a22 4500 445869135 CHVBK 20180317145506.0 cr unu---uuuuu 170323e20110401xx s 000 0 eng 10.1007/s00605-009-0183-2 doi (NATIONALLICENCE)springer-10.1007/s00605-009-0183-2 Färm David Centre for Mathematical Sciences, Lund University, Box 118, 221 00, Lund, Sweden aut Simultaneously non-convergent frequencies of words in different expansions [Elektronische Daten] [David Färm] We consider expanding maps such that the unit interval can be represented as a full symbolic shift space with bounded distortion. There are already theorems about the Hausdorff dimension for sets defined by the set of accumulation points for the frequencies of words in one symbolic space at a time. We show that the dimension is preserved when such sets defined using different maps are intersected. More precisely, it is proven that the dimension of any countable intersection of sets defined by their sets of accumulation for frequencies of words in different expansions, has dimension equal to the infimum of the dimensions of the sets that are intersected. As a consequence, the set of numbers for which the frequencies do not exist has full dimension even after countable intersections. We also prove that this holds for a dense set of non-integer base expansions. Springer-Verlag, 2009 Interval map nationallicence Non-typical point nationallicence Hausdorff dimension nationallicence Beta shift nationallicence Monatshefte für Mathematik Springer Vienna 162/4(2011-04-01), 409-427 0026-9255 162:4<409 2011 162 605 https://doi.org/10.1007/s00605-009-0183-2 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00605-009-0183-2 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Färm David Centre for Mathematical Sciences, Lund University, Box 118, 221 00, Lund, Sweden aut NATIONALLICENCE 773 0- Monatshefte für Mathematik Springer Vienna 162/4(2011-04-01), 409-427 0026-9255 162:4<409 2011 162 605 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer