Dimension of countable intersections of some sets arising in expansions in non-integer bases

Tom 209 / 2010

David Färm, Tomas Persson, Jörg Schmeling Fundamenta Mathematicae 209 (2010), 157-176 MSC: Primary 37E05; Secondary 37C45, 11J83. DOI: 10.4064/fm209-2-4

Streszczenie

We consider expansions of real numbers in non-integer bases. These expansions are generated by $\beta $-shifts. We prove that some sets arising in metric number theory have the countable intersection property. This allows us to consider sets of reals that have common properties in a countable number of different (non-integer) bases. Some of the results are new even for integer bases.

Autorzy

  • David FärmInstitute of Mathematics
    Polish Academy of Sciences
    Śniadeckich 8
    00-956 Warszawa, Poland
    and
    Centre for Mathematical Sciences
    Lund University
    Box 118
    SE-22100 Lund, Sweden
    e-mail
  • Tomas PerssonInstitute of Mathematics
    Polish Academy of Sciences
    Śniadeckich 8
    00-956 Warszawa, Poland
    e-mail
  • Jörg SchmelingCentre for Mathematical Sciences
    Lund University
    Box 118
    SE-22100 Lund, Sweden
    e-mail

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