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

Färm, David LU ; Persson, Tomas LU orcid and Schmeling, Jörg LU (2010) In Fundamenta Mathematicae 209. p.157-176
Abstract (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.
Please use this url to cite or link to this publication:
author
; and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
beta-shift, Hausdorff dimension, non-typical points
in
Fundamenta Mathematicae
volume
209
pages
157 - 176
publisher
Instytut Matematyczny
external identifiers
  • wos:000283036500004
  • scopus:78649529286
ISSN
0016-2736
DOI
10.4064/fm209-2-4
language
English
LU publication?
yes
id
c53b7487-240a-43a0-ac89-32df885b42bb (old id 1668596)
alternative location
http://www.maths.lth.se/matematiklth/personal/tomasp/pub/2009_3.pdf
date added to LUP
2016-04-01 14:56:57
date last changed
2025-10-14 10:01:36
@article{c53b7487-240a-43a0-ac89-32df885b42bb,
  abstract     = {{<b>Abstract in Undetermined</b><br/><br>
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.}},
  author       = {{Färm, David and Persson, Tomas and Schmeling, Jörg}},
  issn         = {{0016-2736}},
  keywords     = {{beta-shift; Hausdorff dimension; non-typical points}},
  language     = {{eng}},
  pages        = {{157--176}},
  publisher    = {{Instytut Matematyczny}},
  series       = {{Fundamenta Mathematicae}},
  title        = {{Dimension of Countable Intersections of Some Sets Arising in Expansions in Non-Integer Bases}},
  url          = {{http://dx.doi.org/10.4064/fm209-2-4}},
  doi          = {{10.4064/fm209-2-4}},
  volume       = {{209}},
  year         = {{2010}},
}