Non-typical points for β-shifts
Färm, David LU and Persson, Tomas LU
(2013)
In Bulletin of the Polish Academy of Sciences: Mathematics
61(2).
p.123-132
- Abstract
- We study sets of non-typical points under the map fβ↦βx mod 1 for non-integer β and extend our results from [Fund. Math. 209 (2010)] in several directions. In particular, we prove that sets of points whose forward orbit avoid certain Cantor sets, and the set of points for which ergodic averages diverge, have large intersection properties. We observe that the technical condition β>1.541 found in the above paper can be removed.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/4251331
- author
- Färm, David
LU
and Persson, Tomas
LU
- organization
- publishing date
- 2013
- type
- Contribution to journal
- publication status
- published
- subject
- in
- Bulletin of the Polish Academy of Sciences: Mathematics
- volume
- 61
- issue
- 2
- pages
- 123 - 132
- publisher
- Institute of Mathematics, Polish Academy of Sciences
- ISSN
- 0239-7269
- DOI
- 10.4064/ba61-2-5
- language
- English
- LU publication?
- yes
- id
- 5916e410-0a4d-41e6-8a7f-92752b6aee77 (old id 4251331)
- alternative location
- https://arxiv.org/abs/1004.4812
- date added to LUP
- 2016-04-01 12:56:45
- date last changed
- 2019-05-24 19:19:53
@article{5916e410-0a4d-41e6-8a7f-92752b6aee77,
abstract = {{We study sets of non-typical points under the map fβ↦βx mod 1 for non-integer β and extend our results from [Fund. Math. 209 (2010)] in several directions. In particular, we prove that sets of points whose forward orbit avoid certain Cantor sets, and the set of points for which ergodic averages diverge, have large intersection properties. We observe that the technical condition β>1.541 found in the above paper can be removed.}},
author = {{Färm, David and Persson, Tomas}},
issn = {{0239-7269}},
language = {{eng}},
number = {{2}},
pages = {{123--132}},
publisher = {{Institute of Mathematics, Polish Academy of Sciences}},
series = {{Bulletin of the Polish Academy of Sciences: Mathematics}},
title = {{Non-typical points for β-shifts}},
url = {{http://dx.doi.org/10.4064/ba61-2-5}},
doi = {{10.4064/ba61-2-5}},
volume = {{61}},
year = {{2013}},
}