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Dimension of Countable Intersections of Some Sets Arising in Expansions in Non-Integer Bases

På svenska

Author

Summary, in Swedish

Abstract in Undetermined

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.

Department/s

Publishing year

2010

Language

English

Pages

157-176

Publication/Series

Fundamenta Mathematicae

Volume

209

Document type

Journal article

Publisher

Institute of Mathematics, Polish Academy of Sciences

Topic

  • Mathematics

Keywords

  • beta-shift
  • Hausdorff dimension
  • non-typical points

Status

Published

Research group

  • Analysis and Dynamics
  • Dynamical systems

ISBN/ISSN/Other

  • ISSN: 0016-2736