Dimension of Countable Intersections of Some Sets Arising in Expansions in Non-Integer Bases
Färm, David LU ; Persson, Tomas LU
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:
https://lup.lub.lu.se/record/1668596
- author
- Färm, David
LU
; Persson, Tomas
LU
and Schmeling, Jörg
LU
- organization
- publishing date
- 2010
- 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
- Institute of Mathematics, Polish Academy of Sciences
- 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
- 2022-03-22 02:41:40
@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 = {{Institute of Mathematics, Polish Academy of Sciences}},
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}},
}