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

David Färm, Tomas Persson, and Jörg Schmeling. "Dimension of countable intersections of some sets arising in expansions in non-integer bases." Fundamenta Mathematicae 209.2 (2010): 157-176. <http://eudml.org/doc/283185>.

@article{DavidFärm2010,
abstract = {We consider expansions of real numbers in non-integer bases. These expansions are generated by β-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.},
author = {David Färm, Tomas Persson, Jörg Schmeling},
journal = {Fundamenta Mathematicae},
keywords = {beta-shift; Hausdorff dimension; non-typical points},
language = {eng},
number = {2},
pages = {157-176},
title = {Dimension of countable intersections of some sets arising in expansions in non-integer bases},
url = {http://eudml.org/doc/283185},
volume = {209},
year = {2010},
}

TY - JOUR
AU - David Färm
AU - Tomas Persson
AU - Jörg Schmeling
TI - Dimension of countable intersections of some sets arising in expansions in non-integer bases
JO - Fundamenta Mathematicae
PY - 2010
VL - 209
IS - 2
SP - 157
EP - 176
AB - We consider expansions of real numbers in non-integer bases. These expansions are generated by β-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.
LA - eng
KW - beta-shift; Hausdorff dimension; non-typical points
UR - http://eudml.org/doc/283185
ER -