Dimension of countable intersections of some sets arising in expansions in non-integer bases
Volume 209 / 2010
Fundamenta Mathematicae 209 (2010), 157-176
MSC: Primary 37E05; Secondary 37C45, 11J83.
DOI: 10.4064/fm209-2-4
Abstract
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.
