Dimension of Countable Intersections of Some Sets Arising in Expansions in Non-Integer Bases
Författare
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.
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.
Avdelning/ar
- Matematik LTH
- Dynamical systems
Publiceringsår
2010
Språk
Engelska
Sidor
157-176
Publikation/Tidskrift/Serie
Fundamenta Mathematicae
Volym
209
Länkar
Dokumenttyp
Artikel i tidskrift
Förlag
Institute of Mathematics, Polish Academy of Sciences
Ämne
- Mathematics
Nyckelord
- beta-shift
- Hausdorff dimension
- non-typical points
Status
Published
Forskningsgrupp
- Analysis and Dynamics
- Dynamical systems
ISBN/ISSN/Övrigt
- ISSN: 0016-2736